Question

Two circles touch externally the sum of their areas is 58 per CM square and distance between the centre is 10 cm find the radii of the two circles.

Answer 1

Answer:

3 cm and 7 cm

Step-by-step explanation:

Let the radii be a and b.

Since the circles touch and the distance between their centres is 10,

a+b = 10

Since the sum of their areas is 58π cm²,

πa² + πb² = 58π      =>      a²+b² = 58

=> a² + (10-a)² = 58

=> 2a² - 20a + 100 = 58

=> 2a² - 20a + 42 = 0

=> a² - 10a + 21 = 0

=> ( a - 3 ) ( a - 7 ) = 0

=> a = 3 or a = 7

If a = 3 then b = 7, and if a = 7 then b = 3.

So the radii of the circles are 3 cm and 7 cm.