MathDB

tangent perpendicular to line, starting with a pentagon incribed in a circle

Source: KJMO 2013 p2

May 1, 2019

geometrypentagonperpendiculartangentcircles

Problem Statement

A pentagon

ABCDE

is inscribed in a circle

O

, and satises

AB = BC , AE = DE

. The circle that is tangent to

DE

E

and passing

A

hits

EC

F

and

BF

G (\ne F)

. Let

DG\cap O = H (\ne D)

. Prove that the tangent to

O

E

is perpendicular to

HA