Equations of tangents of circles

A complete lesson or two on finding equations of tangents to circles with centre the origin. Aimed at the new GCSE specification, although it could also be used with an A-level group.

Activities included:

Starter:
Two recap questions on necessary prerequisites, the first on equations of circles, the second on equations of perpendicular lines. If pupils really struggled with this I would stop and address these issues, rather than persist with the rest of the lesson.

Main:

• A set of questions on finding the gradient of OP, given some point P on a circle, followed by a related worksheet for pupils to practice.
• A follow-up ‘reverse’ task where pupils find points P such that the gradient of OP takes certain values. The intention is that pupils can do this task by logic and geometric reasoning, rather than by forming and solving formal equations, although the task could be further extended to look at this.
• The focus then shifts to gradients of tangents, and finally equations of tangents, with examples and a related set of questions for pupils to practice.
• An extension task where pupils find the equation of the circle given the tangent.

Plenary:
A spot the mistake question.

Printable worksheets and answers included.

Please review if you buy as any feedback is appreciated!