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प्रश्न
Two circles touch each other externally. The sum of their areas is 74π cm2 and the distance between their centers is 12 cm. Find the diameters of the circle.
उत्तर
Let the radius of the circles be r1 and r2.
So, r1 + r2 = 12 ⇒ r2 = 12 - r1
Sum of the areas of the circles = 74π
⇒ πr12 + πr12 = 74π
⇒ r12 + r12 = 74
⇒ r12 + ( 12 - r1 )2 = 74
⇒ r12 + 144 - 24r1 + r12 = 74
⇒ 2r12 - 24r1 + 70 = 0
⇒ r12 - 12r1 + 35 = 0
⇒ ( r1 - 7 )( r1 - 5 ) = 0
⇒ r1 = 7 or r1 = 5
Ir r1 = 7 cm, then r2 = 5 cm
If r1 = 5 cm, then r2 = 7 cm
So, the diameters of the circles will 10 cm and 14 cm.
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