How can you accurately construct the inscribed circle of a right-angled triangle?

Diagram shows blue circle inside a right-angled triangle, touching in 3 places

Labelling the diagram can often help you to break down a problem and to see what’s going on.

  • How could you use the version of the diagram shown below to help?
  • What else can you label on this diagram?
Triangle now has vertices A,B,C and three perpendiculars have been added that touch at the centre of the circle

Can you use this sequence of diagrams to form a chain of mathematical reasoning that will help you to solve the problem?

Try to describe each diagram in turn, using mathematical language where appropriate. A printable version is available here.

Diagram Description