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M=max of BPR, APQ, PQCR. Minimize M

Source: ISI (BS) 2009 #3

May 10, 2012

geometrygeometry unsolved

Problem Statement

Let

ABC

be a right-angled triangle with

BC=AC=1

. Let

P

be any point on

AB

. Draw perpendiculars

PQ

and

PR

on

AC

and

BC

respectively from

P

. Define

M

to be the maximum of the areas of

BPR, APQ

and

PQCR

. Find the minimum possible value of

M

.

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