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find locus when circle through two points varies

Source: Mongolia 1999 Grade 9 P5

May 4, 2021

geometry

Problem Statement

Let

D

be a point in the angle

ABC

. A circle

\gamma

passing through

B

and

D

intersects the lines

AB

and

BC

at

M

and

N

respectively. Find the locus of the midpoint of

MN

when circle

\gamma

varies.

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