MathDB

Parallel lines

Source: Greek TST 2014-Pr.3.

June 25, 2014

geometrycircumcircletrapezoidgeometry proposed

Problem Statement

Let

ABC

be an acute,non-isosceles triangle with

AB<AC<BC

.Let

D,E,Z

be the midpoints of

BC,AC,AB

respectively and segments

BK,CL

are altitudes.In the extension of

DZ

we take a point

M

such that the parallel from

M

to

KL

crosses the extensions of

CA,BA,DE

at

S,T,N

respectively (we extend

CA

to

A

-side and

BA

to

A

-side and

DE

to

E

-side).If the circumcirle

(c_{1})

of

\triangle{MBD}

crosses the line

DN

at

R

and the circumcirle

(c_{2})

of

\triangle{NCD}

crosses the line

DM

at

P

prove that

ST\parallel PR

.

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