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Nội dung: <blockquote data-quote="NguoiDien" data-source="post: 162121" data-attributes="member: 75">Bài IV<a href="https://onthitoan.com/wp-content/uploads/2014/06/Hanoi20141.png" target="_blank"><img src="https://onthitoan.com/wp-content/uploads/2014/06/Hanoi20141.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /></a> 1. Chứng minh <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-5454bdb027047f858eb91d3fc1737d51_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là hình chữ nhật: <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-3578c77a499319233624ac80a3378dd1_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-d79222042426da8270aec9259f4153b6_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là các đường kính của đường tròn <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-4076db7b5c0bfd9b61a0aacceecfd8b0_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên cắt nhau tại tâm <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-e048258bebce99e3c8a41dacee206416_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là trung điểm mỗi đường. Do đó <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-5454bdb027047f858eb91d3fc1737d51_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là hình bình hành. Mặt khác <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-d67769b45b39486e4bf55cf2cfc72e75_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là góc nội tiếp chắn nửa đường tròn nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-56546ff1ee602d85c14b9ee13615f54e_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Vậy <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-5454bdb027047f858eb91d3fc1737d51_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là hình chữ nhật. 2. Chứng minh <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-4abc48781e8b984409a4457633cd792c_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> thuộc cùng một đường tròn: Do <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-ee761acff355c3147e1e8287689e8190_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (góc nội tiếp chắn cùng một dây cung) <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-8cdc9cd456ebbd7cafa276d3fb0f304a_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (Do tam giác <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-6c8a3f3486dce1f1d111bdd891901146_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> vuông tại <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-bb37b78c388ce0097f18af4b756bded8_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />) <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-0dc48668749d9172cf330eee7b1cbd57_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Mặt khác <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-bfb6f76eb6fd4631c3f100b8c077fd35_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-f90cc269629fcfa6aacb949269e39462_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-aec39994a4473d5e6b7b1bd2e3dae25b_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> tứ giác <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-fe48caf89c8b67617020cdf8bc1dba3d_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là tứ giác nội tiếp (tổng hai góc đối bằng <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-ed5853ab0946258cf9aaf4ed5e0afa20_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />) hay bốn điểm <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-4abc48781e8b984409a4457633cd792c_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nằm trên cùng một đường tròn. 3. Chứng minh <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-ac35e81c01b1a17782293d77fa0b760c_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là trung điểm của <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-b5e4265bb1d86add9b939a51f7558156_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-f92e470078dc5e14b8e9ad22edca4f04_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> song song với <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-8886d94cae10380064e9d2dea9cfb4dd_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />:Do <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-8112fc6dba9f60bdbc933c7b84b74caa_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là trung điểm của <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-d995aa7a7797a4d393af96e8e52d2bad_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />, <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-e048258bebce99e3c8a41dacee206416_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là trung điểm của <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-3578c77a499319233624ac80a3378dd1_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-11f662763f98a29d18e0363580c61386_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> song song với <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-437065cf4149386e7279575b1d3e6eff_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> Mặt khác <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-79a070e0bd27ff92365f75261ba28bfa_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-eea12117b746e78d1c123f7181827069_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> song song với <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-5710a86ee8116727111c8f1f198f1b67_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Do <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-e048258bebce99e3c8a41dacee206416_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là trung điểm <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-3578c77a499319233624ac80a3378dd1_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-ac35e81c01b1a17782293d77fa0b760c_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là trung điểm của <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-5710a86ee8116727111c8f1f198f1b67_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Từ chứng minh trên suy ra <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-30b5015fedfe754d5fe87d26a079609d_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-b6981b8058dcc856d8a3ddfb0bbe186d_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Suy ra <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-f92e470078dc5e14b8e9ad22edca4f04_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-8886d94cae10380064e9d2dea9cfb4dd_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là các tiếp tuyến của đường tròn tại <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-1020a7c7fbde10ab860a70d8486048ec_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-d22f5c8ec299b34f433f9e6e7229a7dc_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-3007bdb3f653548ad63b6a7f858863b3_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> Do tam giác <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-12dea11565e87e9ec0b3357ff11e8ebd_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> vuông tại <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-e048258bebce99e3c8a41dacee206416_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-0aed2a73f583720411900cf8eaefc4f4_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> Tương tự ta có <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-38666112df4b138b56aaff0d0419c9a4_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Như vậy ta có <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-e6861af701455da4f9c52a687f6c8243_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Mà hai góc này ở vị trí đồng vị. Từ đây ta suy ra <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-f92e470078dc5e14b8e9ad22edca4f04_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> song song với <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-8886d94cae10380064e9d2dea9cfb4dd_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> 4. Tìm vị trí của <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-1020a7c7fbde10ab860a70d8486048ec_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> để diện tích <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-ca5bdadc08170154dc4ad8defdd79397_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nhỏ nhất: Ta có <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-6fdfdcb4b9f2d670705e4bf7cac81c47_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> Do <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-39378ad64ea9d0108b185f2eb5283705_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-450bc08f76af71b07b94f714f612b079_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-53bfba4d632ebcc255e08209fac2a6b1_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-968194c19c3c3eef51cf05c749893113_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Khi đó <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-f18ebfc574140923da0accf2f2e4d98d_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> Gọi <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-2a8791167a1d9729ac66f81c74a01fb7_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là trung điểm <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-775c14689eadb26c7ff68ede6eb6b32d_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />, ta có <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-9740d2c927e9d9369a71715ede2b8727_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> Gọi <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-58308ca3dfcc7ce2e278a10062b6ef61_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là chân đường vuông góc kẻ từ <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-bb37b78c388ce0097f18af4b756bded8_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> đến <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-d79222042426da8270aec9259f4153b6_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> thì <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-0db69f96dde95ad0745784fd152ba88a_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> Khi đó <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-7ba6eaa1948976d07cf27d91c69f8e43_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Do <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-d79222042426da8270aec9259f4153b6_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là đường kính của <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-4076db7b5c0bfd9b61a0aacceecfd8b0_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-f8ab3a03b4c4d91783780831cbc06b1e_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nhỏ nhất khi và chỉ khi <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-88c72209a317ec0f4fd93c2d7496c60b_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nhỏ nhất. Mặt khác, <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-c2795791ba1f4dcb82f7323196b3b76e_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-348221d7ce783b54134fc71180e06a66_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nên <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-88c72209a317ec0f4fd93c2d7496c60b_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> nhỏ nhất khi và chỉ khi <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-58308ca3dfcc7ce2e278a10062b6ef61_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> trùng với <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-e048258bebce99e3c8a41dacee206416_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-bb37b78c388ce0097f18af4b756bded8_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> trùng với <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-2a8791167a1d9729ac66f81c74a01fb7_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Khi đó <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-d79222042426da8270aec9259f4153b6_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> song song với <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-213089b252295e9f758507d23db725a7_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> hay <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-d79222042426da8270aec9259f4153b6_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> vuông góc với <img src="https://onthitoan.com/wp-content/ql-cache/quicklatex.com-3578c77a499319233624ac80a3378dd1_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />.</blockquote>

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