Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.
Mensuration
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Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.

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Given: Sum of areas of two circles = 130π cm² The distance between their centres = 14 cm Let and be the radii of 2 circles. Area of the first circle + Area of the second circle = 130π ⇒ A₁ \+ A₂ = 130π ⇒ πr₁² \+ πr₂² = 130π ⇒ π(r₁² \+ r₂²) = 130π ⇒ (r₁² \+ r₂²) = 130 ⇒ r₁² \+ r₂² = 130 ...............(1) Also, since the circles touch externally, the sum of their radii equals the distance between their centers. r₁ \+ r₂ = 14 ⇒ r₁ = 14 \- r₂ Putting the value of r₁ in equation (1), ⇒ (14 \- r₂)² \+ r₂² = 130 ⇒ 14² \+ r₂² \- 2 x 14 x r₂ \+ r₂² = 130 ⇒ 196 \+ 2r₂² \- 28r₂ = 130 ⇒ 196 \+ 2r₂² \- 28r₂ \- 130 = 0 ⇒ 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 cm or 3 cm Using equation (1), we find r₁: If r₂ = 11, then r₁ = 14 \- 11 = 3cm If r₂ = 3, then r₁ = 14 \- 3 = 11cm Hence, the radii of the two circles are 11 cm and 3 cm.

Mathematics

Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.

Mensuration

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Mathematics

Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.

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