Inspired by " No way out, by Brian Charlesworth"

Geometry Level 3

On the same side of a straight line three circles are drawn as follows:

  • A circle with a radius of 4 cm is tangent to the line.
  • The other two circles are identical, and each is tangent to the line and to the other two circles.

What are the possible radii of these two identical circles?

A. \ \, 24 cm only
B. \ \, 20 cm only
C. \ \, 16 cm only
D. \ \, 24 and 20 cm only
E. \ \, 20 and 16 cm only
F. \ \, 16 and 24 cm only
G. \ \, 16, 20, 14 cm only
H.  \ \ No solution


Note: A diagram has not been provided because drawing the correct diagram is part of the problem solving.

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