Question

The three circles C1, C2 and C3 have their centers 01, 02 and 03 on the line L and are
all tangent at the same point. If the diameter of the largest circle is 20 units, what is the
ratio of the area of the largest circle to the area of the smallest circle?​

Answer 1

Answer:

Solution

The diameter of circle C1 is equal to 20 units and therefore its radius is equal to 10 units. The area A of the largest circle C1 is equal to

A = π (10)2

The diameter of circle C2 is equal to the radius of circle C1 which is 10 unis. The diameter of circle C3 is equal to the radius of circle C2 which is 5 units. The radius of circle C3 is equal to 2.5. We now calculate the area B of the smallest circle C3.

B = π (2.5)2

The ratio of A to B is given by

A / B = π (10)2 / π (2.5)2

Simplify

= (10)2 / (2.5)2

= (10 / 2.5)2 = 42 = 16

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