3) cho nửa (O) đường kính AB. trên bán kính OA, OB lần lượt lấy M, N sao cho OM=ON. từ M, N kẻ hai tia song song cắt đường tròn tại C và D. c/m: MC ⊥CD
giúp mk vs ạ mk đang cần gấp
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Ta có: MC // ND (gt)
Suy ra tứ giác MCDN là hình thang
Lại có: OM + AM = ON + BN (= R)
Mà AM = BN (gt)
Suy ra: OM = ON
Kẻ OI ⊥ CD (3)
Suy ra: IC = ID (đường kính dây cung)
Khi đó OI là đường trung bình của hình thang ACDN
Suy ra: OI // MC // ND (4)
Từ (3) và (4) suy ra: MC ⊥ CD, ND ⊥ CD.
Lời giải:
Kẻ đường kính $CT$ của $(O)$ thì $O$ là trung điểm $CT$
Xét tứ giác $CNTM$ có 2 đường chéo $CT,MN$ cắt nhau tại trung điểm $O$ của mỗi đường nên $CNTM$ là hình bình hành.
$\Rightarrow CM\parallel NT$. Mà CM\parallel DN$ nên $DN\parallel NT$ hay $D,N,T$ thẳng hàng.
Ta có: $\widehat{CDN}=\widehat{CDT}=90^0$ (góc nt chắn nửa đường tròn)
$\Rightarrow CD\perp DN$. Mà $DN\parallel MC$ nên $CD\perp MC$ (đpcm)
Hình vẽ:
![](data:image/png;base64,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)