This question popped up in another thread:
ABC is a triangle, right angled at B. A circle is inscribed in it.The lengths of the 2 sides containing the right angle are 6 and 8 cm. Find the radius of the circle.
We will use bob bundy's idea from
1) Use the irregular polygon tool and click points (0,6),(0,0),(8,0) and back to (0,6). That draws the right triangle.
2) Use the angle bisector tool to bisect all three angles of the triangle ABC.
3) Use the intersection tool to find the pint of intersection of two of those bisectors. Point D will be created and this is the incenter. It will be at (2,2).
4) In the input bar enter Distance[D, b],Distance[D, xAxis] and Distance[D, yAxis].
5) Numbers g,h and i will be created all with the value of 2.
6) Use the circle with radius tool and choose D with a radius of 2.
We are done! The drawing is below.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.