The diameters AB and CD and two chords BC and BD are drawn in the circle. We need to prove that ABCD is a square.

In the CBD triangle, the angle CBD = 90, since it is based on the diameter of the circle, and since, according to the condition, BC = BD, the triangle CBD is isosceles and rectangular. The chord AD = CB, and the chord AC = BD, which means AC = AD = BC = BD, and the angles A, B, C, D are equal to 90, since all are based on the diameter of the circle, therefore ABCD is a square, which was required to be proved.