Draw square ABCD, and diagonals AC, BD crossing at O.
Consider triangles DAC and CBD
DA = DC = CB ... (Properties of square)
∠DAC = ∠DCA ... (∇ ADC is isos. AD=CD)
∠DAC = ∠ACB ... (Alt. angles AD parallel to BC)
∠BAC = ∠BCA ... (∇ABC is isos. AB=BC )
Such it can be shown that all angles with diagonals create equal angles of half rt. angle
∠DOC = 1 rt. angle ... Angles of triangle = 2 rt. angles
So all angles at centre are 1 rt. angles
So all triangles are congruent ... 2 angles and incl. side equal
∴ OA = OB = OC = OD