Incenters and Circumcenters

The perpendicular bisectors of △ABC intersect at point D and are shown in blue. If BD is 9 and AE is 6, what is AD? (picture not to scale)

Find the coordinates of the circumcenter of the triangle with the given vertices. A(2,6), B(8,6), C(8,10)

Where is the location of the circumcenter for an equilateral triangle?

The Angle bisectors of ABC intersect at point D. What is the measure of DF?

You and two friends plan to meet. You want the meeting place to be the same distance from each person’s house. Explain how you can use a map to locate the meeting place. You may use the graph below to create a diagram to help and/or as part of your explanation.

You are building a roughly triangular koi pond. You want a fountain in the pond. That way you get aeration of the water to help keep the pond clean. You decide it should be the same distance from each edge of the pond. That gives maximum aeration with minimum water loss to over spray. Where should you place the fountain? Explain your reasoning. You may use the graph below to create a diagram to help and/or as part of your explanation.