2023 WSMO Team Round Problems/Problem 14

Problem

Consider quadrilateral $ABCD$ with circumcircle centered at $O$ . Given $AB=2<CD$ , the circumcircle of $\triangle{ABO}$ is tangent to the circumcircle of $\triangle{COD}$ . The circumcircle of $\triangle{AOD}$ passes through the center of the circumcircle of $\triangle{ABO}$ . Given the radius of the circumcircle of $ABCD$ is $6$ . Denote $M,N$ as the area and perimeter of $ABCD$ respectively, compute $\frac{M}{N}$ . The answer can be expressed in the simplest form of $\frac{p\sqrt{q}}{r}$ . Find $p+q+r$

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2023 WSMO Team Round Problems/Problem 14

Problem

Solution