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Question
Two circles touch each other externally. The sum of their areas is 58πcm2 and the distance between their centres us 10cm. Find the radii of the two circles.
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Solution
Let one of the two circles touching externally have a radius of R and the other have radius r
Given R + r = 10cm.
So, R = 10 - r
The Area of a Circle with radius r = πr2
The Area of a Circle with radius R = πR2
Sum of the areas of the two circles
= πr2 + πR
= π(r2 + R2)
= 58π
⇒ r2 + R2 = 58
⇒ r2 + (10 - r)2 = 58
⇒ r2 + 100 + r2 - 20r = 58
⇒ 2r2 - 20r + 42 = 0
⇒ r2 - 10r + 21 = 0
⇒ r2 - 7r - 3r + 21 = 0
⇒ r(r - 7) -3(r - 7) = 0
⇒ (r - 7)(r - 3) = 0
⇒ r = 7, 3
So, one of the two circles touching externally has a radius of 7cm and the other have radius 3cm.
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