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$CC_1$ bisects $\widehat{QC_1P}$ .

Source: 16-th Hungary-Israel Binational Mathematical Competition 2003

March 30, 2007

geometrycircumcircletrigonometrygeometry unsolved

Problem Statement

Let

ABC

be an acute-angled triangle. The tangents to its circumcircle at

A, B, C

form a triangle

PQR

with

C \in PQ

and

B \in PR

. Let

C_{1}

be the foot of the altitude from

C

\Delta ABC

. Prove that

CC_{1}

bisects

\widehat{QC_{1}P}