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Power of a point practise

Source: Kürschák 2003, problem 1

July 8, 2014

geometrycircumcirclegeometry unsolved

Problem Statement

Draw a circle

k

with diameter

\overline{EF}

, and let its tangent in

E

be

e

. Consider all possible pairs

A,B\in e

for which

E\in \overline{AB}

and

AE\cdot EB

is a fixed constant. Define

(A_1,B_1)=(AF\cap k,BF\cap k)

. Prove that the segments

\overline{A_1B_1}

all concur in one point.

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