Question

two circles touch externally the sum of their areas is 130π square cm and the distance between the centre is 14 cm find the radius of the circle

Answer 1

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Answer 2

Solution:

Since the given circles touch externally, we have

sum of their radii = distance between their centres = 14 cm.

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Let the radii of the given circles be x cm and (14 - x) cm.

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Sum of their areas = [πx² + π(14 - x)²] cm²

.°. πx² + π(14 - x)² = 130π

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→ x² + (14 - x)² = 130

→ 2x² - 28x + 66 = 0

→ x² - 14x + 33 = 0

→ (x-11)(x-3) = 0

→ x - 11 = 0 or x - 3 = 0

⇒x = 11 or x = 3.

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Now, x = 11

→ (14- x) = (14-11) = 3.

And, x = 3 (14-x) = (14-3) = 11.

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Hence, the radii of the given circles are 11 cm and 3 cm.

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Answer:

• the radius of the circle are 11 cm and 3 cm.