Cyclic Quadrilaterals

A quadrilateral ABCD inscribed in a circle as shown in the diagram. (a) The quidrilateral ABCD is known as cyclic quadrilateral.(b) The four vertices of a cyclic quadrilateral touch the circumference of a circle.(c) Based on the above diagram, angle A and angle C as well as angle B and angle D are known as opposite angles. It is given that O is the centre of the circle.(i) Determine whether the following quadrilaterals are cyclic quadrilaterals. Explain your answer.(ii) State the opposite angles that exist if the quadrilateral is a cyclic quadrilateral. Based on the diagram, complete the table. Exterior Angle Corresponding interior opposite angle r t u q Based on the diagram, complete the table. Exterior angle Corresponding interior opposite angle a e d b Form equations for the relationships between the angles in the following diagrams. Find the values of m and n for each of the following.