Solving problems with circles and triangles

This lesson develops the concept of using geometric properties to solve problems. In particular students develop their ability in:

• Solving problems by determining the lengths of the sides in right triangles using trigonometry
• Finding the measurements of shapes by decomposing complex shapes into simpler ones

A diagram shows a circle with one equilateral triangle inside and one equilateral triangle outside. The following questions are posed:

• Calculate the exact ratio of the areas of the two triangles.
• Draw a second circle inscribed inside the small triangle. Find the exact ratio of the areas of the two circles.

The lesson features several examples of student work to use for peer assessment and discussion.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.