MathDB

2016 JBMO Shortlist G7

Source: 2016 JBMO Shortlist G7

October 8, 2017

geometryJBMO

Problem Statement

Let

{AB}

be a chord of a circle

{(c)}

centered at

{O}

, and let

{K}

be a point on the segment

{AB}

such that

{AK<BK}

. Two circles through

{K}

, internally tangent to

{(c)}

at

{A}

and

{B}

, respectively, meet again at

{L}

. Let

{P}

be one of the points of intersection of the line

{KL}

and the circle

{(c)}

, and let the lines

{AB}

and

{LO}

meet at

{M}

. Prove that the line

{MP}

is tangent to the circle

{(c)}

.
Theoklitos Paragyiou (Cyprus)

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