# Circles in Triangles

ID: vibof-kuroz
Illustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
Standards: HSG-C.A.3HSG-CO.C.10
PreviewAnswer Key

9 questions

# Circles in Triangles

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##### The Largest Circle

Use a compass to draw the largest circle you can find that fits inside each triangle.

1)

2)

##### The Inner Circle

3) Mark 3 points and connect them with a straightedge to make a large triangle. The triangle should not be equilateral.

4) Construct the incenter of the triangle.

5) Construct the segments that show the distance from the incenter to the sides of the triangle.

6) Construct a circle centered at the incenter using one of the segments you just constructed as a radius.

7) Would it matter which of the three segments you use?

True or false? Write below.

8) Explain your thinking.

##### Equilateral Centers

9) The image shows an equilateral triangle ﻿$ABC$﻿. The angle bisectors are drawn. The incenter is plotted and labeled ﻿$D$﻿.

Prove that the incenter is also the circumcenter.