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CAT 2023 Slot 2 Solved Paper
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© examsnet.com
Question : 61
Total: 66
A triangle is drawn with its vertices on the circle
C
such that one of its sides is a diameter of
C
and the other two sides have their lengths in the ratio
a
:
b
. If the radius of the circle is
r
, then the area of the triangle is
a
b
r
2
2
(
a
2
+
b
2
)
2
a
b
r
2
a
2
+
b
2
4
a
b
r
2
a
2
+
b
2
a
b
r
2
a
2
+
b
2
Validate
Solution:
Since
B
C
is the diameter of the circle, which implies angle
B
A
C
is 90 degrees. Let
A
B
=
a
c
m
, which implies
A
C
=
b
cm
. Hence,
B
C
=
√
a
2
+
b
2
, which is diameter of the circle (2r).
Hence,
2
r
=
√
a
2
+
b
2
⇒
4
r
2
=
a
2
+
b
2
The area of the triangle is
1
2
×
a
×
b
, which can be written as
⇒
a
⋅
b
2
(
a
2
+
b
2
)
×
(
a
2
+
b
2
)
⇒
a
⋅
b
2
(
a
2
+
b
2
)
×
4
r
2
⇒
a
⋅
b
a
2
+
b
2
×
2
r
2
The correct option is B
© examsnet.com
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