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AP/AQ wanted, diameter, circumcenter 2020 BMT Individual 23

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January 6, 2022
geometryratiodiameter

Problem Statement

Circle Γ\Gamma has radius 1010, center OO, and diameter ABAB. Point CC lies on Γ\Gamma such that AC=12AC = 12. Let PP be the circumcenter of △AOC\vartriangle AOC. Line APAP intersects Γ\Gamma at QQ, where QQ is different from AA. Then the value of APAQ\frac{AP}{AQ} can be expressed in the form mn\frac{m}{n}, where m and n are relatively prime positive integers. Compute m+nm + n.
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