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AD x BI x CH <= AC x BD x OK (2015 HOMC Junior - Senior Q11)

Source:

July 19, 2019
geometryconvex quadrilateralperpendiculars

Problem Statement

Given a convex quadrilateral ABCDABCD. Let OO be the intersection point of diagonals ACAC and BDBD and let I,K,HI , K , H be feet of perpendiculars from B,O,CB , O , C to ADAD, respectively. Prove that AD×BI×CH≤AC×BD×OKAD \times BI \times CH \le AC \times BD \times OK.
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