MathDB

2016 preRMO p6, ray of light reflects on circumference

Source:

August 9, 2019

geometrygeometric transformationreflection

Problem Statement

Suppose a circle

C

of radius

\sqrt2

touches the

Y

-axis at the origin

(0, 0)

. A ray of light

L

, parallel to the

X

-axis, reflects on a point

P

on the circumference of

C

, and after reflection, the reflected ray

L'

becomes parallel to the

Y

-axis. Find the distance between the ray

L

and the

X

-axis.