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Rc'/C's = 3/2 wanted, square and a reflection of a point wrt line

Source: Mathematics Regional Olympiad of Mexico Center Zone 2014 P4

November 11, 2021

geometryreflectionsquareratio

Problem Statement

Let

ABCD

be a square and let

M

be the midpoint of

BC

. Let

C ^ \prime

be the reflection of

C

wrt to

DM

. The parallel to

AB

passing through

C ^ \prime

intersects

AD

R

and

BC

S

. Show that

\frac {RC ^ \prime} {C ^\prime S} = \frac {3} {2}