Question

Two circles of different sizes are drawn below. The diameter of the smaller circle is equal to the radius of the larger circle. The common tangent to both circles is 16cm in length and the distance between the centers is 20cm. Determine the diameter of the larger circle. Complete the diagram with appropriate information to support your solution.

I drew a diagram, and it's a rectangle and then a right triangle between the two circles like in my textbook. I tried solving using a right triangle in the diagram however I'm a bit confused and could use some help! By the way, I gave an example of what the diagram looks like below. Minus the numbers.

Answer 1

Diameter of the larger circle = 48 cm

Explanation:

From the figure attached,

Let the radius of the smaller circle is 'BC' = x.

Then the radius of the large circle 'AD' = 2x

Distance between the centers of the circles 'CD' = 20 cm

Length of the common tangent 'AB' = 16 cm

A construction has been done by drawing a perpendicular CE from C to AD by forming a rectangle ABCE.

Therefore, length of CE = length of AB = 16 units

By applying Pythagoras theorem in right triangle CED,

CD² = CE² + DE²

(20)² = (16)² + x²

400 = 256 + x²

x² = 400 - 256

x = √144

x = 12

Radius of the larger circle = 2x

= 2×12

= 24 cm

Therefore, diameter of the larger circle = 2 × radius

= 2 × 24

= 48 cm