2023 SSMO Team Round Problems/Problem 11

Problem

Let $ABCD$ be a cyclic quadrilateral such that $AC$ is the diameter. Let $P$ be the orthocenter of $ABD$ . Define $X = AB\cup CD$ , and $Y = AD\cup BC$ . If $AB = 8$ , $BC = 1$ , and $CD = 4$ , suppose $\frac{[CBPD]}{[AXY]}=\frac{m}{n}.$ Find $m+n$ .

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2023 SSMO Team Round Problems/Problem 11

Problem

Solution