# Triangles and circles #1

- Author:
- Callum Marshall

## Part A

The diagram below shows a circle drawn through three points.

**Drag any of the three points and observe what happens.****What conjecture can you make?**

## Part B

1. Using an

**algebraic method**show how to find where the perpendicular bisectors of the sides AB and BC of a triangle with vertices at A (-3, 2), B (9, 6) and C (4, -4) meet.2.
a. Verify your result from the previous question using the diagram below by

**constructing the perpendicular bisectors for sides AB and BC.****NOW - Construct the perpendicular bisector on the third side, AC, of the triangle.**b. Describe the relationship between the three perpendicular bisectors you have drawn.3.
a. Using the distance formula, find the distance from

**each of the vertices**of the triangle above to the point where the perpendicular bisectors meet. b. Describe what you notice.**The distance formula is**;4.
a. Use the diagram below to

**investigate**what you have found in Questions 2 AND 3 above. b. What conclusions can you come to about the perpendicular bisectors of a triangle?