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प्रश्न
Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centers is 14 cm. Find the radii of the circles.
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उत्तर
Let the radii of two circles be r1 and r2 respectively.
Sum of the areas of two circles = 130π sq. cm
⇒ πr12 + πr22 = 130π
⇒ r12 + r22 = 130 ….(i)
Also, distance between two radii = 14 cm
⇒ r1 + r2 = 14
⇒ r1 = (14 - r2)
Substituting the value of r1 in (i), we get
(14 - r2)2 + r22 = 130
⇒ 196 - 28r2 + r22 + r22 = 130
⇒ 2r22 - 28r2 + 66 = 0
⇒ r22 - 14r2 + 33 = 0
⇒ r22 - 11r2 - 3r2 + 33 = 0
⇒ r2 (r2 - 11) - 3 (r2 - 11) = 0
⇒ (r2 - 11) (r2 - 3) = 0
⇒ r2 = 11 or r2 = 3
⇒ r1 = 14 - 11 = 3 or r1 = 14 - 3 = 11
Thus, the radii of two circles are 11 cm and 3 cm respectively.
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