2015 IMO Problems/Problem 3
Let be an acute triangle with
. Let
be its circumcircle,
its orthocenter, and
the foot of the altitude from
. Let
be the midpoint of
. Let
be the point on
such that
. Assume that the points
,
,
,
, and
are all different, and lie on
in this order.
Prove that the circumcircles of triangles and
are tangent to each other.
The Actual Problem
Let be an acute triangle with
. Let
be its circumcircle,
its orthocenter, and
the foot of the altitude from
. Let
be the midpoint of
. Let
be the point on
such that
and let
be the point on
such that
. Assume that the points
,
,
,
and
are all different and lie on
in this order. Prove that the circumcircles of triangles
and
are tangent to each other.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
2015 IMO (Problems) • Resources | ||
Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
All IMO Problems and Solutions |