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 IK^{2} + IJ^{2} = 2(R^{2} + d^{2}).
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 illstructured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."
