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Standard X
Mathematics
Question
In the given figure, ABC is right triangle, right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.
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Solution
Verified by Toppr
Given
B
C
=
6
c
m
A
B
=
8
c
m
We know that in right angle triangle is
A
C
2
=
A
B
2
+
B
C
2
A
C
2
=
8
2
+
6
2
A
C
2
=
64
+
36
A
C
2
=
100
A
C
=
10
c
m
Now
Area of
△
A
N
=
Area of
△
O
A
B
+
Area of
△
O
B
C
+
Area of
△
O
C
A
⇒
1
2
×
B
C
×
A
B
=
1
2
×
r
×
A
B
+
1
2
×
A
C
×
r
+
1
2
×
B
C
×
r
⇒
1
2
×
6
×
8
=
1
2
×
8
×
r
+
1
2
×
10
×
r
+
1
2
×
6
×
r
⇒
24
r
=
48
⇒
24
r
=
48
⇒
r
=
2
c
m
Thus the radius of the circle is
2
c
m
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Similar Questions
Q1
In the given figure, ABC is right triangle, right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.
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Q2
In the given figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.