2012 JBMO Problems/Problem 2
Section 2
Let the circles and
intersect at two points
and
, and let
be a common tangent of
and
that touches
and
at
and
respectively. If
and
, evaluate the angle
.
Solution
Let and
be the centers of circles
and
respectively. Also let
be the intersection of
and line
.
Note that is perpendicular to
since
is a tangent of
. In order for
to be perpendicular to
,
must be the point diametrically opposite
. (to be continued.)