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प्रश्न
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.
उत्तर
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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