Question 13
In the adjoining figure, four successively touching circles are placed in the interior of $$\angle AOB$$. The first (smallest) has a radius 7 cm . The third circle has a radius 28 cm . Then the radius of the largest circle (in cm ) is
Solution
Circles inscribed in a fixed angle and touching one another are similar figures scaled from the vertex, so their radii form a geometric progression. With $$r_1 = 7$$ and $$r_3 = 7k^2 = 28$$ we get $$k = 2$$. Hence the fourth radius is $$r_4 = 7 \times 2^3 = 56$$.
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