SAT Math Multiple Choice Practice Question 63: Answer and Explanation
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Question: 63
19. 
In this triangle, AC bisects angle BAD. Find AC. (Figure is not drawn to scale.)
A. 
B. 
C. 
D. 5
E. 10
Correct Answer: E
Explanation:
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.