Difference between revisions of "2000 Pan African MO Problems/Problem 5"
Duck master (talk | contribs) (created page with solution (add diagram?); NOTE: SOLUTION IS INCOMPLETE) |
m (→See also) |
||
Line 9: | Line 9: | ||
{{Pan African MO box | {{Pan African MO box | ||
|year=2000 | |year=2000 | ||
− | | | + | |num-b=4 |
− | |num-a= | + | |num-a=6 |
}} | }} | ||
[[Category:Geometry Problems]] {{stub}} | [[Category:Geometry Problems]] {{stub}} |
Latest revision as of 00:10, 28 January 2023
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 Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All Pan African MO Problems and Solutions |
This article is a stub. Help us out by expanding it.