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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2021 Sharygin Geometry Olympiad
19
19
Part of
2021 Sharygin Geometry Olympiad
Problems
(1)
Intersection of common internal tangents are collinear with P
Source: XVII Sharygin Correspondence P19
3/2/2021
A point
P
P
P
lies inside a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
. Common internal tangents to the incircles of triangles
P
A
B
PAB
P
A
B
and
P
C
D
PCD
PC
D
meet at point
Q
Q
Q
, and common internal tangents to the incircles of
P
B
C
,
P
A
D
PBC,PAD
PBC
,
P
A
D
meet at point
R
R
R
. Prove that
P
,
Q
,
R
P,Q,R
P
,
Q
,
R
are collinear.
geometry
trigonometry