SAT Math Multiple Choice Practice Question 63: Answer and Explanation

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Question: 63


In this triangle, AC bisects angle BAD. Find AC. (Figure is not drawn to scale.)

D. 5
E. 10

Correct Answer: E


E. What a surprise: a special right triangle! ABD is a 30-60-90 right triangle, with BAD measuring 60 degrees. Because AC bisects BAD, both CAD and BAC measure 30 degrees. Hey! That makes ABC a 30-60-90 triangle, too! In triangle ABC, line AB is opposite the 60° angle, which means that it equals the shortest side times . The shortest side, BC, is therefore 5. And the longest side is always twice as long as the shortest side, so AC = 10.

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