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Geometry Mathley 5.2 1/ PQ^2 >= 1/ UV^2 - / AC^2

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June 7, 2020
rectanglegeometrygeometric inequalitycircumcircle

Problem Statement

Let ABCDABCD be a rectangle and U,VU, V two points of its circumcircle. Lines AU,CVAU,CV intersect at PP and lines BU,DVBU,DV intersect at QQ, distinct from PP. Prove that 1PQ2≥1UV2−1AC2\frac{1}{PQ^2} \ge \frac{1}{UV^2} - \frac{1}{AC^2} Michel Bataille
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