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alternate segments IOQM 2022-23 P-1

Source:

October 30, 2022
geometryIOQM

Problem Statement

A triangle ABCABC with AC=20AC=20 is inscribed in a circle ω\omega. A tangent tt to ω\omega is drawn through BB. The distance tt from AA is 2525 and that from CC is 1616.If SS denotes the area of the triangle ABCABC, find the largest integer not exceeding S20\frac{S}{20}
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