Unit 7, Lesson 5
Triangles in Circles
Geometry
5.1
Warm-up
One Perpendicular Bisector
The image shows a triangle.
- Construct the perpendicular bisector of segment
. - Imagine a point
placed anywhere on the perpendicular bisector you constructed. How would the distance from to compare to the distance from to ? Explain your reasoning.
Student Lesson Summary
We saw that some quadrilaterals have circumscribed circles. Is the same true for triangles? In fact, all triangles have circumscribed circles. The key fact is that all points on the perpendicular bisector of a segment are equidistant from the endpoints of the segment.
Suppose we have triangle
In this case, the circumcenter happens to fall inside triangle
circumcenter
The circumcenter of a triangle is the intersection point of all three perpendicular bisectors of the triangle’s sides. It is the center of the triangle’s circumscribed circle.
In this diagram, the circumcenter is point
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