MathDB

Russian geometry

Source: Tuymaada-2005, problem 7

July 25, 2005

geometryincentercircumcircleparallelogrampower of a pointradical axisgeometry proposed

Problem Statement

Let

I

be the incentre of triangle

ABC

. A circle containing the points

B

and

C

meets the segments

BI

and

CI

at points

P

and

Q

respectively. It is known that

BP\cdot CQ=PI\cdot QI

. Prove that the circumcircle of the triangle

PQI

is tangent to the circumcircle of

ABC

.
Proposed by S. Berlov

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