Track / Stage 5 / 19 of 400 #619 of 1964

Problem 619

AIME late

Geometry Difficulty 5.1 Find the answer

2. As shown in Figure 15, it is known that quadrilateral $ABCD$ is inscribed in a circle $\odot O$ with a diameter of 3, diagonal $AC$ is the diameter, diagonal $AC$ intersects $BD$ at point $P$ , $AB=BD$ , and $PC=0.6$ . Find the perimeter of quadrilateral $ABCD$ .
(1999, National Junior High School Mathematics Competition)

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Official solution

Prompt: Connect $B O$ and extend it to intersect $A D$ at point $H$ . Essentially, it is the superposition of an isosceles triangle and similar triangles. Answer: $1+2 \sqrt{2}+\sqrt{3}+\sqrt{6}$ .

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