Question

The sum of the areas of two circles which touch each other externally is 153?. If the sum of their radii is 15, find the ratio of the larger to the smaller radius

Answer 1

Answer:

4:1

Step-by-step explanation:

Let the radius of larger circle be x and smaller circle be y.

Sum of area of two circle = 153π

Area of smaller circle + Area of larger circle = 153π

                                     πx² + πy² = 153π

                               ∴      x² + y² = 153 ----------(1)

Sum of radii is 15

                              ∴   x + y = 15  ----------(2)

solve equation (1) and (2) using substituting method

y = 15 - x

substitute into eq(1)

x² + (15-x)² = 153

2x² -30x + 72 = 0

 x² - 15x + 36 = 0

  (x-12)(x-3) = 0

x = 12 and x = 3

As we assumed x is larger radius

So, x = 12 and y = 3

Now, we find the ratio of larger radii to smaller radii

Ratio$\dfrac{12}{3}\Rightarrow 4:1$

Hence, The ratio is 4:1

Answer 2

Answer:

Step-by-step explanation:

Let the radius of the 2 circles be r1 and r2, then

r1 + r2 = 15 (given)

and

πr²1 + πr²2 = 153π (given)

r1² + r2² = 153

∴ r1² +

(15−r1)² = 153

On solving, we get

r1 = 12, r2 = 3

Required ratio

= 12:3

= 4:1