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India STEMS
2022 India STEMS
STEMS 2022 Math Cat A Qualifier Round
4
Easy Geometry
Easy Geometry
Source: STEMS 2021-22 CaT A P4
December 19, 2021
geometry
Problem Statement
Given
△
A
B
C
\triangle ABC
△
A
BC
with
∠
A
=
1
5
∘
\angle A = 15^{\circ}
∠
A
=
1
5
∘
, let
M
M
M
be midpoint of
B
C
BC
BC
and let
E
E
E
and
F
F
F
be points on ray
B
A
BA
B
A
and
C
A
CA
C
A
respectively such that
B
E
=
B
M
=
C
F
BE = BM = CF
BE
=
BM
=
CF
. Let
R
1
R_1
R
1
be the radius of
(
M
E
F
)
(MEF)
(
MEF
)
and
R
2
R_{2}
R
2
be radius of
(
A
E
F
)
(AEF)
(
A
EF
)
. If
R
1
2
R
2
2
=
a
−
b
+
c
\frac{R_1^2}{R_2^2}=a-\sqrt{b+\sqrt{c}}
R
2
2
R
1
2
=
a
−
b
+
c
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are integers. Find
a
b
c
a^{b^{c}}
a
b
c
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