MathDB

64

Part of 1979 IMO Longlists

Problems(1)

Identity - distance from point on circumcircle to sides

Source: ILL 1979 - Problem 64.

6/5/2011
From point PP on arc BCBC of the circumcircle about triangle ABCABC, PXPX is constructed perpendicular to BCBC, PYPY is perpendicular to ACAC, and PZPZ perpendicular to ABAB (all extended if necessary). Prove that BCPX=ACPY+ABPZ\frac{BC}{PX}=\frac{AC}{PY}+\frac{AB}{PZ}.
geometrycircumcirclegeometry unsolved