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MathLinks Contest 4th
3.3
3.3
Part of
MathLinks Contest 4th
Problems
(1)
0433 geometry 4th edition Round 3 p3
Source:
5/7/2021
Let
A
B
C
ABC
A
BC
be a triangle, and let
C
C
C
be its circumcircle. Let
T
T
T
be the circle tangent to
A
B
,
A
C
AB, AC
A
B
,
A
C
and
C
C
C
internally in the points
F
,
E
F, E
F
,
E
and
D
D
D
respectively. Let
P
,
Q
P, Q
P
,
Q
be the intersection points between the line
E
F
EF
EF
and the lines
D
B
DB
D
B
and
D
C
DC
D
C
respectively. Prove that if
D
P
=
D
Q
DP = DQ
D
P
=
D
Q
then the triangle
A
B
C
ABC
A
BC
is isosceles.
geometry
4th edition