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R^2 = OP x OQ

Source: (2021 -) 2022 Dürer Math Competition Regional E2 https://artofproblemsolving.com/community/c1621671_

November 30, 2022
geometrycircumcircle

Problem Statement

In the acute triangle ABCABC the circle through BB touching the line ACAC at AA has centre PP, the circle through AA touching the line BCBC at BB has centre QQ. Let RR and OO be the circumradius and circumcentre of triangle ABCABC, respectively. Show that R2=OPā‹…OQR^2 = OP \cdot OQ.
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