MathDB

interesting hexagon problem from IZHO 2021

Source: IZHO 2021, P2

January 8, 2021

geometryhexagonizho

Problem Statement

In a convex cyclic hexagon

ABCDEF

,

EC

and

CD=AF

. Diagonals

AC

and

DF

intersect at point

Q,

and diagonals

FR=PD

and

DF

intersect at point

P.

Points

R

and

S

are marked on the segments

PS

and

BF

respectively so that

TC

and

BQ=FS.

The segments

RQ

and

PS

intersect at point

T.

Prove that the line

TC

bisects the diagonal

DB

.

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