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OE x d = r^2, incircle related

Source: Indian Postal Coaching 2009 set 5 p5

May 26, 2020
geometryincircledistance

Problem Statement

Let ABCDABCD be a quadrilateral that has an incircle with centre OO and radius rr. Let P=AB∩CDP = AB \cap CD, Q=AD∩BCQ = AD \cap BC, E=AC∩BDE = AC \cap BD. Show that OE⋅d=r2OE \cdot d = r^2, where dd is the distance of OO from PQPQ.
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