Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 4.6 AIME Find the answer

1. As shown in the figure, $AB$ is the diameter of $\odot O$ , $AB=4$ , chord $BC=3$ , the angle bisector of $\angle ABC$ intersects the semicircle at $D$ , the extensions of $AD$ and $BC$ meet at $E$ . Then the area of quadrilateral $ABCD$ is ( ) times the area of $\triangle DCE$ .
(A) 7 times.
(B) 8 times.
(C) 3 times.
(D) 4 times.

Solution

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