Mathematics
For the three circles with centers A, B and C and radii 5 cm, 2 cm and 6 cm respectively.
Assertion (A) : To find the perimeter of the triangle ABC, add the radii of given three circles.
Reason (R) : The required perimeter is the product of sum of radii by 2.
A is true, R is true
A is true, R is false
A is false, R is true
A is false, R is false
Circles
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Answer
Let the circles intersect at points D, E and F.
From figure,
Perimeter of triangle ABC = AB + BC + CA
= (AD + BD) + (BE + CE) + (CF + FA)
= 5 + 2 + 2 + 6 + 6 + 5
= 26 cm.
On adding radii of three circles, we get :
5 + 2 + 6 = 13 cm, which is not equal to perimeter.
Sum of radii × 2 = 13 × 2 = 26 cm, which is equal to perimeter.
∴ A is false, R is true
Hence, Option 3 is correct option.
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