Prove that a cyclic parallelogram is a rectangle.
ABC and ADC are two right triangles with common hypotenuse AC. Prove that .
If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.
Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see figure). Prove that .
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.