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find the angle , ratio of cevians related to orthocenter given

Source: Greece JBMO TST 2006

May 24, 2019

ratiogeometryorthocenterAngle Chasing

Problem Statement

Find the angle

\angle A

of a triangle

ABC

, when we know it's altitudes

BD

and

CE

intersect in an interior point

H

of the triangle and

BH=2HD

and

CH=HE