MathDB

Perpendicular

Source: Iranian National Olympiad (3rd Round) 2006

September 21, 2006

geometrycircumcircleparallelogramrectanglegeometric transformationgeometry proposed

Problem Statement

ABC

is a triangle and

R,Q,P

are midpoints of

AB,AC,BC

. Line

AP

intersects

RQ

in

E

and circumcircle of

ABC

in

F

.

T,S

are on

RP,PQ

such that

ES\perp PQ,ET\perp RP

.

F'

is on circumcircle of

ABC

that

FF'

is diameter. The point of intersection of

AF'

and

BC

is

E'

.

S',T'

are on

AB,AC

that

E'S'\perp AB,E'T'\perp AC

. Prove that

TS

and

T'S'

are perpendicular.

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