Question

Two circles touch externally , the sum of their
area is 90 pi cm²and distance between their centre
is 6 cm. Find radii of circle.​

Answer 1

Answer:

Wrong data

Step-by-step explanation:

Let r₁ and r₂ be the radii of the circles.

now sum of their area = 90π

⇒ πr₁² + πr₂² = 90π

⇒ r₁² + r₂² = 90 .......(1)

Since the circles touch each other externally, distance between their center is r₁ + r₂. Therefore

r₁ + r₂ = 6 .............(2)

⇒ (r₁ + r₂)² = 6²

⇒ r₁² + r₂² + 2r₁r₂ = 36

⇒ 90 + 2r₁r₂ = 36

The value 90π must have been wrongly typed here as it is not a possible value as you see in the above equation. With the correct value we can calculate value of r₁r₂. Now we can get values of r₁ and r₂ by solving the quaratic equation(after substituting value of r₁ + r₂ and r₁r₂)

x² - (r₁ + r₂)x + r₁r₂ = 0