MathDB

Locus of circumcentre of PQC as C varies

Source: Italy TST 1995

November 22, 2010

geometrycircumcirclegeometric transformationreflectionvectorgeometry proposed

Problem Statement

In a triangle

ABC

P

and

Q

are the feet of the altitudes from

B

and

A

respectively. Find the locus of the circumcentre of triangle

PQC

, when point

C

varies (with

A

and

B

fixed) in such a way that

\angle ACB

is equal to

60^{\circ}