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Geometry Mathley 3.1 OI = OJ

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June 7, 2020
geometryequal segmentscircumcirclecircles

Problem Statement

AB,ACAB,AC are tangent to a circle (O)(O), B,CB,C are the points of tangency. QQ is a point iside the angle BACBAC, on the ray AQAQ, take a point PP suc that OPOP is perpendicular to AQAQ. The line OPOP meets the circumcircles triangles BPQBPQ and CPQCPQ at I,JI, J. Prove that OI=OJOI = OJ.
Hồ Quang Vinh
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