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Giải bài 1 trang 106 vở thực hành Toán 9 tập 2

Cho tam giác ABC có các đường cao AD, BE, CF. Chứng minh rằng BCEF, CAFD, ABDE là những tứ giác nội tiếp.

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

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Đề bài

Cho tam giác ABC có các đường cao AD, BE, CF. Chứng minh rằng BCEF, CAFD, ABDE là những tứ giác nội tiếp.

Phương pháp giải - Xem chi tiết

+ Gọi M là trung điểm của BC. + Chứng minh \(ME = MB = MC = MF\). Suy ra đường tròn \(\left( {M,MB} \right)\) ngoại tiếp tứ giác \(BCEF\). + Chứng minh tương tự ta có \(CAFD\)và \(ABDE\) cũng là các tứ giác nội tiếp.

Lời giải chi tiết

 

Lấy \(M\) là trung điểm của BC. Do \(BCE,BCF\) là các tam giác vuông có chung cạnh huyền \(BC\) nên \(ME = MB = MC = MF\). Do đó đường tròn \(\left( {M,MB} \right)\) ngoại tiếp tứ giác \(BCEF\). Tương tự, \(CAFD\) và \(ABDE\) cũng là các tứ giác nội tiếp.

  • 𝐆 Giải bài 2 trang 106 vở thực hành Toán 9 tập 2 Cho tứ giác ABCD nội tiếp đường tròn (O), AB cắt CD tại E, AD cắt BC tại F như hình sau đây. Biết (widehat {BEC} = {40^o}) và (widehat {DFC} = {20^o}), tính số đo các góc của tứ giác ABCD.
  • 🧜 Giải bài 3 trang 107 vở thực hành Toán 9 tập 2 Cho hình vuông ABCD có cạnh bằng 4cm. Tính chu vi, diện tích của các đường tròn nội tiếp và ngoại tiếp hình vuông ABCD.
  • 🎶 Giải bài 4 trang 108 vở thực hành Toán 9 tập 2 Biết rằng bốn đỉnh A, B, C, D của một hình vuông cùng nằm trên một đường tròn (O) theo thứ tự ngược chiều kim đồng hồ. Phép quay thuận chiều ({45^o}) biến các điểm A, B, C, D lần lượt thành các điểm E, F, G, H. a) Vẽ đa giác EAFBGCHD. b) Đa giác EAFBGCHD có phải là một hình bát giác đều hay không? Vì sao?
  • 𝔉 Giải bài 5 trang 108 vở thực hành Toán 9 tập 2 Cho ngũ giác đều ABCDE nội tiếp đường tròn (O) như hình bên. a) Hãy tìm một phép quay thuận chiều tâm O biến điểm A thành điểm C. b) Phép quay trên sẽ biến các điểm B, C, D, E lần lượt thành những điểm nào? Phép quay này có giữ nguyên ngũ giác đều ABCDE không?
  • 🍸 Giải bài 6 trang 109 vở thực hành Toán 9 tập 2 Người ta muốn làm một khay đựng bánh kẹo hình lục giác đều có cạnh 10cm và chia thành 7 ngăn gồm một lục giác đều nhỏ và 6 hình thang cân như hình dưới đây. Hỏi lục giác đều nhỏ phải có cạnh bằng bao nhiêu để nó có diện tích bằng hai lần diện tích mỗi hình thang?
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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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