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INAMO 2019 P6 - Ez Geo

Source: INAMO 2019 P6

July 3, 2019
Inamogeometrypower of a point

Problem Statement

Given a circle with center OO, such that AA is not on the circumcircle. Let BB be the reflection of AA with respect to OO. Now let PP be a point on the circumcircle. The line perpendicular to APAP through PP intersects the circle at QQ. Prove that AP×BQAP \times BQ remains constant as PP varies.
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