Inspired by " No way out, by Brian Charlesworth"
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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Here is a rough sketch of the problem's condition. I hope many would have got the 'hint' in the 'note'
Lets concentrate on the part that has the solution.
In the △ O ′ N A we have O ′ A 2 = O ′ N 2 + A N 2 . Or ( r + 4 ) 2 = r 2 + ( r − 4 ) 2 , solving which gives the value of r = 1 6 , 0