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fixed point for a line, statring with intersecting circles

Source: IV Soros Olympiad 1997-98 R3 9.11 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 1, 2024

geometryfixedFixed point

Problem Statement

Given two circles intersecting at points

A

and

B

. A certain circle touches the first at point

A

, intersects the second at point

M

and intersects the straight line

AB

at point

P

(

M

and

P

are different from

B

). Prove that the straight line

MP

passes through a fixed point of the plane (for any change in the third circle).