A circle centered at B is tangent to AC. In triangle ABC, AB = 6, BC = 8 and CA = 12. What is the radius of this circle?
Hint: Use Heron's formula to calculate the area, then use this formula (h = 2*A / a) to find the radius.
The altitude from point B to line segment AC is the radius of a circle.
Here is another way, (though Heron's formula is probably easier.
Let X be the point of intersection of the circle and the tangent
Let r be the radius
Now you have triangles BCX and BAX
The angles at X are right angles so you can use pythagoras's theorum to find XC and XA in terms of r
added they equal 12
(it is a bit tricky)