9.11

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(1)

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

Given two circles intersecting at points

A

B

. A certain circle touches the first at point

A

, intersects the second at point

M

and intersects the straight line

AB

P

M

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).

geometryfixedFixed point