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Prove an eq triangle

Source: Indian RMO 2000 Problem 1

October 26, 2005

analytic geometryparallelogramIBO 2k14

Problem Statement

Let

AC

be a line segment in the plane and

B

a points between

A

and

C

. Construct isosceles triangles

PAB

and

QAC

on one side of the segment

AC

such that

\angle APB = \angle BQC = 120^{\circ}

and an isosceles triangle

RAC

on the other side of

AC

such that

\angle ARC = 120^{\circ}.

Show that

PQR

is an equilateral triangle.

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