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.

Given: Sum of areas of two circles = 130π cm 2 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 ⇒ A 1 \+ A 2 = 130π ⇒ πr 1 2 \+ πr 2 2 = 130π ⇒ π(r 1 2 \+ r 2 2 ) = 130π ⇒ (r 1 2 \+ r 2 2 ) = 130 ⇒ r 1 2 \+ r 2 2 = 130 ...............(1) Also, since the circles touch externally, the sum of their radii equals the distance between their centers. r 1 \+ r 2 = 14 ⇒ r 1 = 14 \- r 2 Putting the value of r 1 in equation (1), ⇒ (14 \- r 2 ) 2 \+ r 2 2 = 130 ⇒ 14 2 \+ r 2 2 \- 2 x 14 x r 2 \+ r 2 2 = 130 ⇒ 196 \+ 2r 2 2 \- 28r 2 = 130 ⇒ 196 \+ 2r 2 2 \- 28r 2 \- 130 = 0 ⇒ 2r 2 2 \- 28r 2 \+ 66 = 0 ⇒ r 2 2 \- 14r 2 \+ 33 = 0 ⇒ r 2 2 \- 11r 2 \- 3r 2 \+ 33 = 0 ⇒ r 2 (r 2 \- 11) \- 3(r 2 \- 11) = 0 ⇒ (r 2 \- 11)(r 2 \- 3) = 0 ⇒ r 2 = 11 cm or 3 cm Using equation (1), we find r 1 : If r 2 = 11, then r 1 = 14 \- 11 = 3cm If r 2 = 3, then r 1 = 14 \- 3 = 11cm Hence, the radii of the two circles are 11 cm and 3 cm.

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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.

Mensuration

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A steel wire, when bent in the form of a square, encloses an area of 121 cm². The same wire is bent in the form of a circle. Find area of the circle.

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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.

Mensuration

Related Questions

A steel wire, when bent in the form of a square, encloses an area of 121 cm2. The same wire is bent in the form of a circle. Find area of the circle.

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A steel wire, when bent in the form of a square, encloses an area of 121 cm². The same wire is bent in the form of a circle. Find area of the circle.

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.