A 2011 IMO Tangency Problem

​
rotate M
2.55
Let
ABC
be an acute triangle with circumcircle
Γ
. Let
l
be a tangent line to
Γ
at the point
M
and let
l
a
,
l
b
, and
l
c
be the lines obtained by reflecting
l
in the lines
BC
,
CA
, and
AB
, respectively. Let
A'B'C'
be the triangle formed by the intersections of
l
a
,
l
b
, and
l
c
. Then the circumcircle of
A'B'C'
is tangent to the circle
Γ
.

Details

This is problem 6 in the 2011 International Mathematical Olympiad; see International Mathematical Olympiad Problems.

External Links

Acute Triangle (Wolfram MathWorld)
Circumcircle (Wolfram MathWorld)
Reflection (Wolfram MathWorld)
Tangent Circles (Wolfram MathWorld)
Tangent Line (Wolfram MathWorld)

Permanent Citation

Jay Warendorff
​
​"A 2011 IMO Tangency Problem"​
​http://demonstrations.wolfram.com/A2011IMOTangencyProblem/​
​Wolfram Demonstrations Project​
​Published: August 29, 2011