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Identity - distance from point on circumcircle to sides

Source: ILL 1979 - Problem 64.

June 5, 2011

geometrycircumcirclegeometry unsolved

Problem Statement

From point

P

on arc

BC

of the circumcircle about triangle

ABC

PX

is constructed perpendicular to

BC

PY

is perpendicular to

AC

, and

PZ

perpendicular to

AB

(all extended if necessary). Prove that

\frac{BC}{PX}=\frac{AC}{PY}+\frac{AB}{PZ}