Circle Theorem 4


Theorem 4

The opposite angles in a cyclic quadrilateral add up to In plain terms: If you look at the cyclic quadrilateral (a four sided shape where the four vertices touch the circumference of a circle) below, each vertex is a point on the circumference of the circle. I have divided the quadrilateral down the middle with a dotted line (take note that the line does not pass through the centre of the circle so it does not represent the diameter of the circle). The dotted line divides the quadrilateral into two triangles. Remember, all the internal angles of a triangle add up to . Therefore, all the internal angles of a cyclic quadrilateral will add up to If you add Angle and Angle the result will always be equal to + = If you add up the angles for the remaining two unknown angles then that will also equal Scroll all the way down for more information!
What else is there to say? I'll tell you... Take a look at the graphic below and note the relationship between Angle and Angle ( and )and the relationship between Angle and Angle ( and ) = and = Does this remind you of anything? It should because if you look back at Circle Theorem 2 then you will see the relationship between two adjacent vertices, the arc between them and the other two vertices on the opposite side of the circle.