# Where Can The Perpendicular Bisectors Of The Sides Of A Right Triangle Intersect?

#### Can The Perpendicular Bisectors Of The Sides Of A Right Triangle Intersect?

The perpendicular bisectors of the sides of a right triangle can intersect inside, on, or outside the triangle. The point where they meet is called the circumcenter and is equidistant from each of the three vertices.

During this activity, students will compare the circumcenters of acute, obtuse, and right triangles. They will find that the circumcenter of a right triangle lies on its hypotenuse, the circumcenter of an acute triangle lies inside the triangle, and the circumcenter of an obtuse triangle lies outside the triangle.

In this activity, students will use the tools provided to measure the distances between the vertices of each triangle and draw circles that pass through each of the 3 vertices. They will then determine where the circle lands on each of the vertices.

As they work, students will identify the location of the circumcenter in each triangle and explain why it is located there. They may also need to rehearse what they will say when they share their findings with the rest of the class.

The purpose of this activity is to help students develop a deeper understanding of the concept of a circumscribed circle, how a circle passes through all vertices of a triangle, and that a circleâ€™s center is the intersection of all its perpendicular bisectors. Students will be able to discuss the significance of these concepts and apply them to their own lives.

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