Question

JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the nearest hundredth. (Hint: Show that triangles LMJ and LKJ are right triangles, and then use right triangle trigonometry to solving for missing sides of the right triangles.)

Answer 1

In the problem of insufficient data quantities. I can get a general  solution.We know that tangent to a circle is perpendicular to the radius at the point of tangency. It's mean that triangles LJM and LJK are rights.

Let angle JLK like X.

So, angle JLM=61-x.

And it's mean that by using right triangle trigonometry 

Radius MJ = LM*cos(61-X)