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प्रश्न
Two circles touch each other externally. The sum of their areas is 5811 cm2 and the distance between their centres is 10 cm. Find the radii of the two circles.
उत्तर
Let r be radius of one drde, so the radius of other drde is
(10-r)
Sum of the areas = π r2 + π (10 - r)2
⇒ π r2 + π (10 - r)2 = 58 π
⇒ π r2 + π (100 - 20 r + r2) = 58 π
⇒ r2 + 100 - 20 r + r2 = 58
⇒ 2r2 + 100 - 20 r - 58 = 0
⇒ 2r2 - 20 r + 42 = 0
⇒ r2 - 10 r + 21 = 0
⇒ (r - 7)(r - 3) = 0
⇒ r = 7 , r = 3
Therefore, radii of the two circles is ?cm and 3 cm
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