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Find the locus of Miquel point

Source: KoMaL A.748

May 18, 2019

geometryincircleMiquel point

Problem Statement

The circles

\Omega

and

\omega

in its interior are fixed. The distinct points

A,B,C,D,E

move on

\Omega

in such a way that the line segments

AB,BC,CD,DE

are tangents to

\omega

.The lines

AB

and

CD

meet at point

P

, the lines

BC

and

DE

meet at

Q

. Let

R

be the second intersection of the circles

BCP

and

CDQ

, other than

C

. Show that

R

moves either on a circle or on a line.

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