# Incenter - 2019

- Author:
- Rebecca Young

- Topic:
- Geometry

## Follow the steps below to construct the incenter on the triangle given above.

**Step 1:**Use to construct the angle bisectors of angles A, B and C.

**Step 2:**Use to add a point where the three angle bisectors intersect.

**Step 3:**Use to label the point where the angle bisectors intersect.

**The point where all three angle bisectors intersect is called the incenter.
**
1. No matter how you move the triangle, the **incenter** is always inside the triangle. Use to adjust the triangle. What do you notice about vertex A if it is very close to the **incenter**?

- A
- B
- C

2. Use to adjust the triangle so that one vertex is definitely farther from the **incenter** than the other vertices. What do you notice about the angle measure of that vertex in relation to the other vertices?

- A
- B
- C

Use to draw the segment from the **incenter** to point D.
Use to draw the segment from the **incenter** to point E
Use to draw the segment from the **incenter** to point F.
3. These segments show the shortest distance from the **incenter** to each side of the triangle. Measure the angle between each segment and the triangle side it intersects. What do you notice?

- A
- B
- C

## Incenter Properties

Use to measure the length of each segment from the incenter.
Use to drag a vertex of the triangle around.
4. What do you notice about the distance from the **incenter** to each side of the triangle?

## The Circle

Construct a circle that is inside the triangle and touches each side of the triangle once.
5. Why do you think the name **incenter** was given to the point we are exploring in this activity?

## Application for Incenter

6. For which of the following situations, would it make sense to find the **incenter**?

- A
- B
- C