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2 fixed lines and 2 fixed points, 2 parallel segments, locus of intersection

Source: Sharygin 2006 IX- X CR 13

August 23, 2019

LocusgeometryLocus problemslinesparallel

Problem Statement

Two straight lines

a

and

b

are given and also points

A

and

B

. Point

X

slides along the line

a

, and point

Y

slides along the line

b

, so that

AX \parallel BY

. Find the locus of the intersection point of

AY

with

XB