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Giải bài 24 trang 92 sách bài tập toán 9 - Cánh diều tập 2

Cho hình bình hành ABCD. Đường tròn đi qua ba điểm A, B, C cắt cạnh CD ở P (P khác C và D). Tìm phát biểu sai: A. AP = AD B. Tứ giác ABCP là hình thang cân C. (widehat {APD} = widehat {ABC}) D. (widehat {PCB} + widehat {BAP} < {180^o})

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

🔯Cho hình bình hành ABCD. Đường tròn đi qua ba điểm A, B, C cắt cạnh CD ở P (P khác C và D). Tìm phát biểu sai:

A. AP = AD

B. Tứ giác ABCP là hình thang cân

C. \(\widehat {APD} = \widehat {ABC}\)

🌺D. \(\widehat {PCB} + \widehat {BAP} < {180^o}\)

Phương pháp giải - Xem chi tiết

Trong một tứ giác nội tiếp, tổng hai góc đối bằng 180o.

Lời giải chi tiết

Ta có ABCD là hình bình hành suy ra \(\widehat B + \widehat C = {180^o}\) (hai góc trong cùng phía) (1) ABCP là tứ giác nội tiếp suy ra \(\widehat B + \widehat {APC} = {180^o}\) (2) Từ (1) và (2) suy ra \(\widehat B = \widehat {PAB}\) hay ABCP là hình thang cân. Suy ra AP = BC (3) mà ABCD là hình bình hành nên AD = BC (4) Từ (3) và (4) suy ra AP = AD. Vì ABCP nội tiếp nên \(\widehat {PCB} + \widehat {BAP} = {180^o}\). Chọn đáp án D.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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