More triangles and circles

1. Using the diagram below, construct the angle bisectors for the triangle shown. Hint: USE THREE POINTS rather than selecting the two arms of the angle to construct the angle bisector.

2. Drag any of the vertices of your triangle; describe what you notice about the three angle bisectors.

3. In the diagram below a circle has been constructed inside the triangle shown such that it is the largest circle possible within the bounds of the triangle.

a. Construct the centre of the circle; b. Construct the angle bisectors of the triangle. Drag any of the vertices of the triangle - what do you notice?