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Question
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.
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Solution
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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