Is It Cyclic?

Part of the Circles section of Coddy's Geometry journey. Lesson 44 of 62.

The 180° rule holds only when all four corners are on the circle. Move one corner off the circle, inside or outside, and the opposite angles no longer have to add to 180°. Before you use the rule, look at every corner.

$Quadrilateral ABCD with C inside the circle, not on it$

Here A, B and D are on the circle but C is inside it. The angle at A is 80°, but the angle at C is not fixed by it: slide C around inside and it changes. So the answer to whether you can find it is No. Compare a quadrilateral with all four corners on the circle, where 80° at A would give 100° at C.

Challenge

A, B and C are on circle O, and D is inside it. The angle at A is marked. Is there enough information to find the angle at C? Answer, then press Check.

Try it yourself

$Is there enough information?$

Is there enough information?

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Is It Cyclic?

All lessons in Circles