MathDB

11

Part of 2015 Hanoi Open Mathematics Competitions

Problems(1)

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

Source:

7/19/2019
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.
geometryconvex quadrilateralperpendiculars