# 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 . 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
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*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*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.

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