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Byju's Answer
Standard X
Mathematics
Area of a Circle
The given fig...
Question
The given figure shows a circle (with centre
O
) inscribed in a right-angled triangle
A
B
C
with
∠
B
=
90
∘
,
A
B
=
8
c
m
and
B
C
=
6
c
m
. Find:
i) the radius of the circle
ii) the area of the shaded portion enclosed between the circle and the triangle.
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Solution
(
1
)
A
C
=
√
6
2
+
8
2
=
10
c
m
s
=
10
+
6
+
8
2
=
12
r
=
√
(
5
−
a
)
(
5
−
b
)
(
5
−
c
)
s
=
√
2
×
6
×
4
12
=
2
(
r
a
d
i
u
s
o
f
i
n
s
c
r
i
b
e
d
c
i
r
c
l
e
)
(
2
)
a
r
e
a
o
f
s
h
a
d
e
d
p
o
r
t
i
o
n
=
a
r
e
a
o
f
Δ
−
a
r
e
a
o
f
c
i
r
c
l
e
=
1
2
×
8
×
6
−
π
(
2
)
2
=
24
−
4
π
=
4
(
6
−
π
)
c
m
2
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