MathDB

Cyclic hexagon with two equal sides

Source: Netherlands IMO Team Selection Test 2013

October 21, 2014

geometrycircumcirclesymmetrygeometry unsolved

Problem Statement

Let

ABCDEF

be a cyclic hexagon satisfying

AB\perp BD

and

BC=EF

.Let

P

be the intersection of lines

BC

and

AD

and let

Q

be the intersection of lines

EF

and

L

.Assume that

P

and

Q

are on the same side of

D

and

A

is on the opposite side.Let

S

be the midpoint of

AD

.Let

K

and

L

be the incentres of

\triangle BPS

and

\triangle EQS

respectively.Prove that

\angle KDL=90^0

.

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