Difference between revisions of "2015 IMO Problems/Problem 3"
m (Corrected LaTeX) |
(Added IMO box and category) |
||
| Line 2: | Line 2: | ||
Prove that the circumcircles of triangles <math>KQH</math> and <math>FKM</math> are tangent to each other. | Prove that the circumcircles of triangles <math>KQH</math> and <math>FKM</math> are tangent to each other. | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=2015|num-b=2|num-a=4}} | ||
| + | |||
| + | [[Category:Olympiad Geometry Problems]] | ||
Revision as of 01:36, 31 December 2019
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.
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 | ||
