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 circles 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{In }\Delta O^{1}CP\\ & O^{1}P=\sqrt{{20}^2+{15}^2}=25\text{ cm}\\ & OP=25-15-r=10-r\\ & \text{In }\Delta OPD\&\Delta O^{1}CP\\ & \frac{OP}{O^{1}P}=\frac{OD}{O^{1}C}\\ & \frac{10-r}{25}=\frac{r}{15}\\ & 150-15r=25r\\ & r=\frac{150}{40}\\ & r=3.75\text{ cm}\end{array}$$