P20

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

locus with reflections on 2 perpendicular lines

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

Given a right-angled triangle

y_C

and two perpendicular lines

x

y

passing through the vertex

A

of its right angle. For an arbitrary point

X

x

y_B

y_C

as the reflections of

y

XB

XC

respectively. Let

y_c

be the common point of

y_b

y_c

. Find the locus of

Y

y_b

y_c

do not coincide).

geometryLocusgeometric transformationreflection