**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:

$\displaystyle (3+x)^2=8^2+(5+x)^2-2(8)(5+x)cos 60$

$\displaystyle 9+6x+x^2=64+25+10x+x^2-80-x$

$\displaystyle 4x=64+25+40-9$

$\displaystyle x=10$

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!

**12**In any triangle ABC, prove:

**a)**$\displaystyle a^2-b^2=c(a cos B - b cos A)$

**b)**$\displaystyle c= a cos B + b cos A$

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

Any help would be greatly appreciated!