Inscribing and circumscribing right triangles

This is a concept development lesson that develops thinking on decomposing complex shapes into simpler ones in order to solve a problem. There is work on bringing together several geometric concepts to solve a problem. Students also find the relationship between radii of inscribed and circumscribed circles of right triangles.

A diagram is shows a circle that passes through all three vertices of a triangle (a circumscribed circle). The largest circle that fits inside the triangle is drawn (an inscribed circle). The triangle has sides 5 units, 12 units and 13 units. Students begin by calculating the radii of the circumscribed and inscribed circles.

An extension task is to show how the radii of circumscribed and inscribed circles can be calculated for right triangle with any lengths.

The task assumes that students are familiar with all of the circle theorems.

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.