AMC8 2005
AMC8 2005 · Q9
AMC8 2005 · Q9. It mainly tests Triangles (properties).
In quadrilateral ABCD, sides AB and BC both have length 10, sides CD and DA both have length 17, and the measure of angle ADC is 60°. What is the length of diagonal AC?
在四边形 ABCD 中，边 AB 和 BC 长度均为 10，边 CD 和 DA 长度均为 17，角 ADC 的度量为 60°。对角线 AC 的长度是多少？
(A)
13.5
13.5
(B)
14
14
(C)
15.5
15.5
(D)
17
17
(E)
18.5
18.5
Answer
Correct choice: (D)
正确答案：（D）
Solution
(D) Triangle $ACD$ is an isosceles triangle with a $60^\circ$ angle, so it is also equilateral. Therefore, the length of $AC$ is $17$.
（D）三角形 $ACD$ 是一个含有 $60^\circ$ 角的等腰三角形，因此它也是等边三角形。所以，$AC$ 的长度是 $17$。
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