AMC10 2010 B

AMC10 2010 B · Q6

AMC10 2010 B · Q6. It mainly tests Triangles (properties), Circle theorems.

A circle is centered at $O$, $AB$ is a diameter and $C$ is a point on the circle with $\angle COB=50^\circ$. What is the degree measure of $\angle CAB$?

一个圆以 $O$ 为圆心，$AB$ 是直径，$C$ 是圆上一点，且 $\angle COB=50^\circ$。$\angle CAB$ 的度数是多少？

(A) 20 20

(B) 25 25

(D) 50 50

(E) 65 65

Answer

Correct choice: (B)

正确答案：（B）

Solution

Note that $\angle AOC=180^\circ-50^\circ=130^\circ$. Because $\triangle AOC$ is isosceles, $\angle CAB=\frac{1}{2}(180^\circ-130^\circ)=25^\circ$.

注意到 $\angle AOC=180^\circ-50^\circ=130^\circ$。因为 $\triangle AOC$ 是等腰三角形，$\angle CAB=\frac{1}{2}(180^\circ-130^\circ)=25^\circ$。

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