Prove that any non-isosceles trapezium is not cyclic.

Prove that diagonals of trapezium cut each other proportionally.

Prove that any outer angle of a cyclic quadrilateral is equal to the inner angle at the opposite vertex.

Prove that any outer. angle of a cyclic quadrilateral is equal to the interior angle, at the opposite vertex.

Prove that a parallelogram which is not a rectangle is not cyclic.

In the figure AB is a chord and CD is the diameter perpendicular to it. Prove that ABC is, an Isosceles triangle.

The coordinates of the vertices of a triangle are (3,5), (9,13), (10,6), Prove that this triangle is isosceles. Calculate its area.