There are two circles C1 and C2 of radii 3 and 8 units respectively. The common internal tangent, T, touches the circles at points P1 and P2 respectively. The line joining the centers of the circles intersects T at X. The distance of X from the center of the smaller circle is 5 units. What is the length of the line segment P1P2?
Explanation:
Let A, B be the centre of the two circles with radius 3cm, 8cm respectively.
AX = 5cm, AP1 = 3cm
Using Pythagoras theorem, P1X = 4cm
Now ∆ A P1X ≈ ∆ B P2X
⇒ A P1/ B P2 = P1X/ P2X
⇒ 3/8 = 4/ P2X
P2X = 10.66
P1 P2 = P1X + P2X = 14.66
Hence, option (c).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.