MathDB

TST Geometry P7

Source: Turkey Team Selection Test 2019 Day 3 Problem 7

March 26, 2019

geometry

Problem Statement

In a triangle

ABC

with

\angle ACB = 90^{\circ}

D

is the foot of the altitude of

C

. Let

E

and

F

be the reflections of

D

with respect to

AC

and

BC

. Let

O_1

and

O_2

be the circumcenters of

\triangle {ECB}

and

\triangle {FCA}

. Show that:

2O_1O_2=AB

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