# Two circles touch each other at point X. Two common tangents of the

| Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

A. 3.5

B. 3.75

C. 4.25

D. 4.45

### Right Answer is: B

#### SOLUTION

Let the radius of small circle be O’D = r

In Δ OBP

Let

In Δ OBP &Δ O’DP

∠ P = ∠ P (Common)

∠ OBP = ∠ O’DP (90^{O})

∠ BOP = ∠ DO’P (Third angle)

Δ OBP ~ Δ O’DP

cm

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Two circles touch each other at point X. Two common tangents of the