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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 3.75
CP = 20 cm = PB, AB = 15 cm
AP = √(202+152) = 25 cm
AF = 15 + r
PF = 25 - (15 + r) = (10 - r) cm
△ABP ~ △FEP
So,
AB/FE = AP/FP
⇒ 15/r = 25/(10-r)
⇒ 5r = 30-3r
⇒ r = 30/8 = 15/4 = 3.75 cm