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University of Nottingham
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Circles in triangles
The task shows a circle or radius r that just touches the sides of a right triangle whose sides are 3 units, 4 units, and 5 units long. A square is constructed from the right angle with length r so that one of its vertices is at the centre of the circle. Further lines are constructed from the centre of the circle to the remaining vertices. Questions follow on proving the congruence of the triangles that have been constructed and the lengths of line segments.
An extension question requires students to produce similar augments for a 5, 12, 13 triangle.
This task is from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. A full rubric is given for the task, together with examples of student work and suggestions for helping students overcome misconceptions. Further information on the collection is given here.
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