You are going to investigate quadrilaterals that have inscribed circles as shown in the diagram.

Draw a circle with any radius you choose, and then draw 4 tangents making a quadrilateral with the circle inside touching the quadrilateral at 4 points.

Measure the edge lengths of the quadrilateral ABCD.

What do you notice?

Copy the table below with 8 columns and write the details of your own special quad in the first row. You could try this with different quadrilaterals that touch the same circle or with different circles.

What do you notice? Write down your own conjecture.

Can you prove your conjecture?

Now draw the radii to the points of contact E, F, G & H, each in their own quad, and then to measure the angles.

What do you notice?

Now draw segment AO. Can you prove that Δ AEO ≡ Δ AGO?

Compare lengths AG and AE.

Click here for Notes for Teachers.

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