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collinear wanted, circumcircle related

Source: Dutch IMO TST1 2012 p5

August 6, 2019

geometryangle bisectorcircumcircle

Problem Statement

Let

\Gamma

be the circumcircle of the acute triangle

ABC

. The angle bisector of angle

ABC

intersects

AC

in the point

B_1

and the short arc

AC

of

\Gamma

in the point

P

. The line through

B_1

perpendicular to

BC

intersects the short arc

BC

of

\Gamma

in

K

. The line through

B

perpendicular to

AK

intersects

AC

in

L

. Prove that

K, L

and

P

lie on a line.

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