MathDB

Problem 6

Source: All-Russian Olympiad 2019 grade 10 Problem 6

April 24, 2019

geometrycircumcircle

Problem Statement

Let

L

be the foot of the internal bisector of

\angle B

in an acute-angled triangle

ABC.

The points

D

and

E

are the midpoints of the smaller arcs

AB

and

BC

respectively in the circumcircle

\omega

of

\triangle ABC.

Points

P

and

Q

are marked on the extensions of the segments

BD

and

BE

beyond

D

and

E

respectively so that

\measuredangle APB=\measuredangle CQB=90^{\circ}.

Prove that the midpoint of

BL

lies on the line

PQ.

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