MathDB

SMT 2021 Geometry #6

Source:

August 9, 2023

geometry

Problem Statement

\odot A

, centered at point

D

, has radius

E

and

\odot A

, centered at point

F

, has radius

EC

.

AB = 13

. The circles intersect at points

C

and

D

. Let

E

be a point on

\odot A

, and

F

be the point where line

EC

intersects

\odot B

, again. Let the midpoints of

DE

and

DF

be

M

and

N

, respectively. Lines

AM

and

BN

intersect at point

G

. If point

E

is allowed to move freely on

\odot A

, what is the radius of the locus of

G

?

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