2

Part of 2007 Flanders Math Olympiad

Problems(1)

Source: 2007 Flanders Math Olympiad, Problem 2

Given is a half circle with midpoint

O

AB

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

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