Great angle chase

In this activity, students are presented with a complex diagram of a circle with chords, a tangent and a diameter. Some angle measurements are included in the diagram.

The task is to find the size of every angle in the diagram. The problem can be solved without adding extra lines to the diagram but students should be discouraged from attempting this strategy.

You may wish to give some of the following hints to assist students who are experiencing difficulty with the problem.

• Locate the centre of the circle and apply theorems which mention the centre.
• Locate any cyclic quadrilaterals and apply appropriate theorems.
• Focus on each chord and locate each angle at the circumference that is standing on it.
• Locate angles between tangents and chords and then find the angles in the alternate segment.

Encourage your students to work in pencil so that errors can be easily corrected on the diagram.

Some of the angle relationships are difficult to visualise and so a step-by-step Great angle chase slide show presentation of a possible solution strategy can be downloaded. You can download the complete Great angle chase solutions.

There is also a supplementary worksheet called Putting it all together for you to use with your class.