Question

Two circles touch each other externally. The sum of their areas is 5811 cm² and the distance between their centres is 10 cm. Find the radii of the two circles.

Answer 1

Let r be radius of one drde, so the radius of other drde is
(10-r)

Sum of the areas = π r² + π (10 - r)² 

⇒ π r² + π (10 - r)² = 58 π

⇒ π r² + π (100 - 20 r + r²) = 58 π

⇒ r² + 100 - 20 r + r² = 58

⇒ 2r² + 100 - 20 r - 58 = 0

⇒ 2r² - 20 r + 42 = 0

⇒ r² - 10 r + 21 = 0

⇒ (r - 7)(r - 3) = 0

⇒ r = 7 , r = 3

Therefore, radii of the two circles is ?cm and 3 cm