In the plane we are given two circles intersecting at
and
. Prove that there exist four points with the following property:
(P) For every circle touching the two given circles at
and
, and meeting the line
at
and
, each of the lines
,
,
,
passes through one of these points.
%V0
In the plane we are given two circles intersecting at $X$ and $Y$. Prove that there exist four points with the following property:
(P) For every circle touching the two given circles at $A$ and $B$, and meeting the line $XY$ at $C$ and $D$, each of the lines $AC$, $AD$, $BC$, $BD$ passes through one of these points.
Školjka