Triangles and circles #1
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?