Question

two circles touch internally sum of their areas is 73 π cm2 and the distance between their centre is 5 cm find the radii of the circles​

Answer 1

Step-by-step explanation:

areas=73 =5cm=pie are square =22/7x 73x73=16,746.4=5 cm=radius =X/2= 5/2=2.5

Answer 2

Answer:

The radii of the circles are 3, and 8.

Step-by-step explanation:

Assumption,

Let the Radius of the big circle and radius of the small circle be R and r.

Given,

The sum of areas of two circles is 73π cm².

The distance between their centers (d) is 5 cm.

To find,

The radii of the circles R, and r.

Calculation,

A1 + A2 = 73π

⇒ πR² + πr² = 73π

⇒ R² + r² = 73...(1)

But also we know that the distance between their centers d is:

d = R - r

R - r = 5

⇒ R = 5 + r we substitute in equation (1)

(5 + r)² + r² = 73

⇒ 25 + r² + 10r + r² = 73

⇒ r² + 5r - 24 = 0

⇒ r = 3

Hence, R = 5 + r = 5 + 3 = 8

Therefore, the radii of the circles are 3, and 8.

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