Two circles touch each other externally. The sum of their areas is 74π cm² and the distance between their centres is 12 cm. Find the diameters of the circle.
Mensuration
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Two circles touch each other externally. The sum of their areas is 74π cm² and the distance between their centres is 12 cm. Find the diameters of the circle.

KnowledgeBoat · Accepted Answer

Given: Sum of area = 740π cm² The distance between their centres = 12 cm Let and be the radius of 2 circles. ⇒ A₁ \+ A₂ = 74π ⇒ πr₁² \+ πr₂² = 74π ⇒ π(r₁² \+ r₂²) = 74π ⇒ (r₁² \+ r₂²) = 74 ⇒ r₁² \+ r₂² = 74 ...............(1) And, r₁ \+ r₂ = 12 ⇒ r₁ = 12 \- r₂ Putting the value of r₁ in equation (1), ⇒ (12 \- r₂)² \+ r₂² = 74 ⇒ 12² \+ r₂² \- 2 x 12 x r₂ \+ r₂² = 74 ⇒ 144 \+ 2r₂² \- 24r₂ = 74 ⇒ 144 \+ 2r₂² \- 24r₂ \- 74 = 0 ⇒ 2r₂² \- 24r₂ \+ 70 = 0 ⇒ r₂² \- 12r₂ \+ 35 = 0 ⇒ r₂² \- 7r₂ \- 5r₂ \+ 35 = 0 ⇒ r₂(r₂ \- 7) \- 5(r₂ \- 7) = 0 ⇒ (r₂ \- 7)(r₂ \- 5) = 0 ⇒ r₂ = 7 cm or 5 cm ⇒ r₁ = 12 \- r₂ = 12 \- 7 or 12 \- 5 = 5 cm or 7 cm Hence, the radius of 2 circles = 7 cm and 5 cm.

Mathematics

Two circles touch each other externally. The sum of their areas is 74π cm² and the distance between their centres is 12 cm. Find the diameters of the circle.

Mensuration

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Mathematics

Two circles touch each other externally. The sum of their areas is 74π cm2 and the distance between their centres is 12 cm. Find the diameters of the circle.

Mensuration

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