MathDB

Centroamerican 2018, problem 2

Source: 2018 Centroamerican and Caribbean Math Olympiad

June 25, 2018

geometryCentroamericangeometric transformationreflection

Problem Statement

Let

\Delta ABC

be a triangle inscribed in the circumference

\omega

of center

BT'

. Let

T

be the symmetric of

C

respect to

O

and

T'

be the reflection of

T

respect to line

AB

. Line

BT'

intersects

\omega

again at

R

. The perpendicular to

CT

through

O

intersects line

AC

at

L

. Let

N

be the intersection of lines

TR

and

AC

. Prove that

\overline{CN}=2\overline{AL}

.

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