Question

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

a. 25
b. 26
c. 27
d. 28

Answer 1

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

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=√(d^2-(r_1-r_2)^2)`

`24=√(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.