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International Contests
Pan-African Shortlist
2018 Pan-African Shortlist
G2
G2
Part of
2018 Pan-African Shortlist
Problems
(1)
Intersection of tangents to circles passing through two vertices of a triangle
Source: 2018 Pan-African Shortlist - G2
5/7/2019
Let
P
P
P
be a point on the median
A
M
AM
A
M
of a triangle
A
B
C
ABC
A
BC
. Suppose that the tangents to the circumcircles of
A
B
P
ABP
A
BP
and
A
C
P
ACP
A
CP
at
B
B
B
and
C
C
C
respectively meet at
Q
Q
Q
. Show that
∠
P
A
B
=
∠
C
A
Q
\angle PAB = \angle CAQ
∠
P
A
B
=
∠
C
A
Q
.
geometry
Tangents
Triangle