In a bicentric quadrilateral ABCD, I
is the incenter, O the circumcenter, R the circumradius, and IO
= d. BI
and DI extended meet the circumcircle O at J and K,
respectively. Prove that IK2 + IJ2 = 2(R2 + d2).
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."