2000 Pan African MO Problems/Problem 5
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Let be circle and let
be a point outside
. Let
and
be the tangents from
to
(where
). A line passing through
intersects
at points
and
. Let
be a point on
such that
. Prove that
bisects
.
Solution
There is a projective transformation which maps to a circle and that maps the midpoint of
to its center (EXPAND); therefore, we may assume without loss of generality that the midpoint of
is the center of
. But then
is the reflection of
across
, so that
is the antipode of
on
, and we are done.
See also
2000 Pan African MO (Problems) | ||
Preceded by First Problem |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
All Pan African MO Problems and Solutions |
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