Cho (O) có dây AB vuông góc với dây CD . Gọi M là trung điểm của BC . C/M OM = 1/2 AD?

By Trang Ánh Nam -



Giải:
Vẽ đường kính BG
Ta có:
ü Góc Clớn +góc Cnhỏ =90 độ
ü Góc D+ góc A =90
=>góc Clớn = góc D (lưu ý những góc ở trên hình có đủ đường thẳng tạo thành T mới xem là góc – vì nó cần thiết, các bạn tự kí hiệu và trình bày theo ý của mình. Đây chỉ là bài mẫu.)
=>số đo cung DAG = số đo cung CGA
=>SỐ đo cung DA= số đo cung CG  (trừ cung AG ra)
=>DA=CG  (1)
Tam giác BGC có:
ü M là trung điểm của BC (gt)
ü O là trung điễm của BG (BG là đường kính đường tròn tâm O)
=>OM là đường trung bình
=>OM=CG/2   (2)
Từ (1) và (2) suy ra:
OM=AD/2

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