[Trang Ánh Nam] New comment on Ôn thi Tuyển Sinh 10 - Phần Hình Học.

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Câu 39: [Hưng Yên 2014 – 2015]

Cho ABC có ba góc nhọn nội tiếp trong đường tròn tâm O, bán kính R. Hạ các đường cao AH, BK của tam giác. Các tia AH, BK lần lượt cắt (O) tại các điểm thứ hai là D, E.
a) Chứng minh tứ giác ABHK nội tiếp đường tròn . Xác định tâm đường tròn đó.
b) Chứng minh : HK // DE.
c) Cho (O) và dây AB cố định, điểm C di chuyển trên (O) sao cho tam giác ABC có ba góc nhọn. Chứng minh rằng độ dài bán kính đường tròn ngoại tiếp  CHK không đổi.


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Posted by Trang Ánh Nam to Trang Ánh Nam at February 12, 2019 at 3:25 AM

[Trang Ánh Nam] New comment on Ôn thi Tuyển Sinh 10 - Phần Hình Học.

Trang Ánh Nam has left a new comment on your post "Ôn thi Tuyển Sinh 10 - Phần Hình Học":

Câu 38: [Hưng Yên 2016 – 2017]
Cho đường tròn (O) đường kính AB. Trên tiếp tuyến tại A của đường tròn lấy điểm C sao cho C khác A. Từ C kẻ tiếp tuyến thứ hai CD (D là tiếp điểm) và cát tuyến CMN (M nằm giữa N và C) với đường tròn. Gọi H là giao điểm và CO và AD.
a) Chứng minh các điểm C, A, O, D cùng nằm trên một đường tròn.
b) Chứng minh CH.CO = CM.CN
c) Tiếp tuyến tại Mcuar đường tròn (O) cắt CA, CD thứ tự tại E, F. Đường thẳng vuông góc với OC tại O cắt CA, CD thứ tự tại P, Q. Chứng minh PE + QF >= PQ.


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Posted by Trang Ánh Nam to Trang Ánh Nam at February 12, 2019 at 3:25 AM

[Trang Ánh Nam] New comment on Ôn thi Tuyển Sinh 10 - Phần Hình Học.

Trang Ánh Nam has left a new comment on your post "Ôn thi Tuyển Sinh 10 - Phần Hình Học":

Câu 37: [Hòa Bình 2014 – 2015]

Cho tứ giác ABCD nội tiếp đường tròn (O) đường kính AD. Hai đường chéo AC và BD cắt nhau tại E. Kẻ EF vuông góc với AD ( F ∈ AD )
a) Chứng minh rằng tia CA là phân giác của góc BCF.
b) Gọi M là trung điểm của DE. Chứng minh rằng: CM.DB = DF.DO


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Posted by Trang Ánh Nam to Trang Ánh Nam at February 12, 2019 at 3:24 AM

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