Two circles touch each other externally. The sum of their areas is 74π cm 2 and the distance between their centres is 12 cm. Find the diameters of the circle.

Given: Sum of area = 740π cm 2 The distance between their centres = 12 cm Let and be the radius of 2 circles. ⇒ A 1 \+ A 2 = 74π ⇒ πr 1 2 \+ πr 2 2 = 74π ⇒ π(r 1 2 \+ r 2 2 ) = 74π ⇒ (r 1 2 \+ r 2 2 ) = 74 ⇒ r 1 2 \+ r 2 2 = 74 ...............(1) And, r 1 \+ r 2 = 12 ⇒ r 1 = 12 \- r 2 Putting the value of r 1 in equation (1), ⇒ (12 \- r 2 ) 2 \+ r 2 2 = 74 ⇒ 12 2 \+ r 2 2 \- 2 x 12 x r 2 \+ r 2 2 = 74 ⇒ 144 \+ 2r 2 2 \- 24r 2 = 74 ⇒ 144 \+ 2r 2 2 \- 24r 2 \- 74 = 0 ⇒ 2r 2 2 \- 24r 2 \+ 70 = 0 ⇒ r 2 2 \- 12r 2 \+ 35 = 0 ⇒ r 2 2 \- 7r 2 \- 5r 2 \+ 35 = 0 ⇒ r 2 (r 2 \- 7) \- 5(r 2 \- 7) = 0 ⇒ (r 2 \- 7)(r 2 \- 5) = 0 ⇒ r 2 = 7 cm or 5 cm ⇒ r 1 = 12 \- r 2 = 12 \- 7 or 12 \- 5 = 5 cm or 7 cm Hence, the radius of 2 circles = 7 cm and 5 cm.

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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

Related Questions

The perimeter of a semicircular plate is 108 cm, find its area.

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.

If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

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

Related Questions

The perimeter of a semicircular plate is 108 cm, find its area.

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.

If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

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.