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
[tex]l=\sqrt{d^2-(r_1-r_2)^2}[/tex]
[tex]24=\sqrt{d^2-(10-3)^2}[/tex]
Square both sides.
[tex]576=d^2-49[/tex]
[tex]625=d^2[/tex]
Take square root both sides.
[tex]25=d[/tex]
Therefore length of MN is 25 and option a is correct.
