In a bicentric quadrilateral ABCD, AB,
BC, CD, and AD are tangent to the incircle at E,
F, G, and H. Prove that EG
and FH are perpendicular.
A bicentric quadrilateral ABCD is a convex quadrilateral that has both an incircle
I and a circumcircle O.
Geometry problem solving is one of the
most challenging skills for students to learn. When a problem
requires auxiliary construction, the difficulty of the problem
increases drastically, perhaps because deciding which
construction to make is an ill-structured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."