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2013 BMT Spring
10
BMT 2013 Spring - Geometry 10
BMT 2013 Spring - Geometry 10
Source:
December 29, 2021
geometry
Problem Statement
Let
D
,
E
D, E
D
,
E
, and
F
F
F
be the points at which the incircle,
ω
\omega
ω
, of
△
A
B
C
\vartriangle ABC
△
A
BC
is tangent to
B
C
BC
BC
,
C
A
CA
C
A
, and
A
B
AB
A
B
, respectively.
A
D
AD
A
D
intersects
ω
\omega
ω
again at
T
T
T
. Extend rays
T
E
T E
TE
,
T
F
T F
TF
to hit line
B
C
BC
BC
at
E
′
E'
E
′
,
F
′
F'
F
′
, respectively. If
B
C
=
21
BC = 21
BC
=
21
,
C
A
=
16
CA = 16
C
A
=
16
, and
A
B
=
15
AB = 15
A
B
=
15
, then find
∣
1
D
E
′
−
1
D
F
′
∣
\left|\frac{1}{DE'} -\frac{1}{DF'}\right|
D
E
′
1
−
D
F
′
1
.
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