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Manipal Entrance Test 2013 Math Paper
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© examsnet.com
Question : 70
Total: 80
In an equilateral triangle, the in-radius, circum-radius and one o f the ex-radii are in the ratio
2 : 3 : 5
1 : 2 : 3
1 : 3 : 7
3 : 7 : 9
Validate
Solution:
We have;
Δ
=
√
3
4
a
2
,
s
=
3
a
2
∴
r
=
Δ
S
=
a
2
√
3
,
R
=
a
b
c
4
Δ
=
a
3
√
3
.
a
2
=
a
√
3
and
r
1
=
Δ
S
−
a
=
√
3
∕
4
.
a
2
a
∕
2
=
√
3
2
.
a
Hence;
r
:
R
:
r
1
=
a
2
√
3
:
a
√
3
:
√
3
2
.
a
=
1
:
2
:
3
© examsnet.com
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