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Line passes through the touching points of incircle

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-6 (Grade-8-9)

May 1, 2017

geometry

Problem Statement

Let

ABCD

be a convex quadrilateral with

AC = BD = AD

;

E

and

F

the midpoints of

AB

and

CD

respectively;

O

the common point of the diagonals.Prove that

EF

passes through the touching points of the incircle of triangle

AOD

with

AO

and

OD

Proposed by N.Moskvitin