the sides of a triangle are a=13cm b=14cm and c=15cm.the sides a and b are the tangents to a circle whose centre lies on the third side,then the circumference of the circle is
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The sides of the triangle are given as
a = 13 cm
b = 14 cm
c = 15 cm
Circumference of a circle = C = ?
Solution:
Since we know that,
C = 2 π r .......... (1)
Where 'r' is the radius which is to be calculated.
We also know that,
Area = A = r . P/2
⇒ r = 2 A / P ........ (2)
Perimeter = P = 13 + 14 + 15 = 42 cm
P/2 = 42/2 = 21 cm
Area = A = √ [ p/2 (p/2-13) (p/2-14) (p/2-15) ]
A = √ [ (21) (8) (7) (6)]
A = √ 7056
A = 84 cm²
Put these values in equation (2), we get:
r = (2) (84) / 42
r = 4 cm
Now put this value in equation (1), we get:
C = (2) (3.14) (4)
C = 25.12 cm
which is the required answer.
a = 13 cm
b = 14 cm
c = 15 cm
Circumference of a circle = C = ?
Solution:
Since we know that,
C = 2 π r .......... (1)
Where 'r' is the radius which is to be calculated.
We also know that,
Area = A = r . P/2
⇒ r = 2 A / P ........ (2)
Perimeter = P = 13 + 14 + 15 = 42 cm
P/2 = 42/2 = 21 cm
Area = A = √ [ p/2 (p/2-13) (p/2-14) (p/2-15) ]
A = √ [ (21) (8) (7) (6)]
A = √ 7056
A = 84 cm²
Put these values in equation (2), we get:
r = (2) (84) / 42
r = 4 cm
Now put this value in equation (1), we get:
C = (2) (3.14) (4)
C = 25.12 cm
which is the required answer.
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