10)Three circles with centres A, B and C are mutually tangent and no circle lies inside another circle. The circle with centre A has a radius of 3 cm and the circle with centre B has a radius of 5 cm.

a)If angle BAC= 60 degrees, determine the radius of the third circle.

b)Find the area of triangle ABC

I drew a picture and went out on a wing and tried to use the cosine law:

Now that's all fine and dandy, but the answer at the back of the book says the answer is 2 cm! I don't know what to do!

12In any triangle ABC, prove:

a)

b)

I don't even know where to start...

Any help would be greatly appreciated!