MathDB

locus with reflections on 2 perpendicular lines

Source: Sharygin Geometry Olympiad 2017 First Round P20 grades 10-11

July 22, 2018

geometryLocusgeometric transformationreflection

Problem Statement

Given a right-angled triangle

ABC

and two perpendicular lines

x

and

y

passing through the vertex

A

of its right angle. For an arbitrary point

X

x

define

y_B

and

y_C

as the reflections of

y

about

XB

and

XC

respectively. Let

Y

be the common point of

y_b

and

y_c

. Find the locus of

Y

(when

y_b

and

y_c

do not coincide).