MathDB
Problems
Contests
International Contests
Pan African
2016 PAMO
1
1
Part of
2016 PAMO
Problems
(1)
PAMO 2016 Q1
Source: PAMO 2016
4/29/2016
Two circles
C
1
\mathcal{C}_1
C
1
and
C
2
\mathcal{C}_2
C
2
intersect each other at two distinct points
M
M
M
and
N
N
N
. A common tangent lines touches
C
1
\mathcal{C}_1
C
1
at
P
P
P
and
C
2
\mathcal{C}_2
C
2
at
Q
Q
Q
, the line being closer to
N
N
N
than to
M
M
M
. The line
P
N
PN
PN
meets the circle
C
2
\mathcal{C}_2
C
2
again at the point
R
R
R
. Prove that the line
M
Q
MQ
MQ
is a bisector of the angle
∠
P
M
R
\angle{PMR}
∠
PMR
.
geometry
common tangents