Question

In the pully system shown in this figure, MQ = 10 in, NP = 3in and QP=24in. Find MN

Answer 1

Answer:

The correct option is a. The length of MN is 25.

Step-by-step explanation:

Given information: MQ = 10 in, NP = 3 in and QP=24 in.

If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is

$l=\sqrt{d^2-(r_1-r_2)^2}$

$24=\sqrt{d^2-(10-3)^2}$

Square both sides.

$576=d^2-49$

$625=d^2$

Take square root both sides.

$25=d$

Therefore  length of MN is 25 and option a is correct.