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Question
The sum of diameters of two circles is 112cm and the sum of their areas is 5236cm2. Find the radii of the two circles.
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Solution
Let one of two circles touching externally have a radius of R and the other have radius r
Given 2R + 2r
= 112cm R + r
= 56cm.
So, R = 56 - 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 + πR2
= π(r2 + R2)
= 5236
⇒ r2 + R2 = 1666
⇒ r2 + 56
⇒ 2r2 - 112r + 1470 = 0
⇒ r2 - 56r + 735 = 0
⇒ r2 - 35r - 21r + 735 = 0
⇒ r(r - 35) - 21(r - 35) = 0
⇒ (r - 35)(r - 21) = 0
⇒ r = 35, 21
So, one of the two circles touching externally has a radius of 35cm and the other has radius 21cm.
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