MathDB

easy geometry

Source: 2007 Flanders Math Olympiad, Problem 2

April 26, 2015

geometrynational olympiadbelgium

Problem Statement

Given is a half circle with midpoint

O

and diameter

AB

. Let

Z

be a random point inside the half circle, and let

X

be the intersection of

OZ

and the half circle, and

Y

the intersection of

AZ

and the half circle.
If

P

is the intersection of

BY

with the tangent line in

X

to the half circle, show that

PZ \perp BX

.

Back to Problems View on AoPS