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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.
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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