A square sheet of paper ABCD is folded with D falling on E along BC, A falling on F and EF intersecting AB at G. A circle is inscribed in triangle GBE with radius R .
Determine FG in terms of R.
Using Geometers' Sketchpad, select E along BC. Connect E to D and erect a perpendicular bisector, and a line through A parallel to DE. Place F the same distance from that perpendicular bisector as A, in the opposite direction. Construct EF to complete the triangle and construct the inscribed circle.
The radius of the inscribed circle is equal to the length of FG no matter how you move E.
FG = R.

Posted by Charlie
on 20140427 15:52:02 