Question

There are two circles $C_1$ and $C_2$ of radii 3 and 8 units respectively. The common internal tangent, T, touches the circles at points $P_1$ and $P_2$ 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 $P_1P_2$?

Accepted Answer

C. In $	riangle OP_1X$, $P_1X = \sqrt{5^2 - 3^2} = 4$. By similar triangles $	riangle OP_1X \sim 	riangle O'P_2X$, $\frac{XP_2}{P_1X} = \frac{O'P_2}{OP_1} = \frac{8}{3} \implies XP_2 = 4 	imes \frac{8}{3} = 10.66$. $P_1P_2 = P_1X + XP_2 = 4 + 10.66 = 14.66$ units.

Common Internal Tangent of Circles

Explanation

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