Curated Video
Finding Circumcenters and Incenters of a Triangle Using Angle Bisectors, Perpendicular Bisectors, and Circles
In this lesson, students will learn how to find the circumcenter and incenter of a triangle using angle bisectors, perpendicular bisectors, and circles. They will understand the concept of different centers in a triangle and how they...
Curated Video
Constructing a Circumscribed Circle on a Triangle Using Perpendicular Bisectors
In this lesson, students will understand that a circumscribed circle is a circle that passes through all the vertices of a polygon, and that its center is where the perpendicular bisectors of the polygon intersect. By following...
Professor Dave Explains
Special Lines in Triangles: Bisectors, Medians, and Altitudes
Working with triangles.
Khan Academy
Khan Academy: Geometry: Euler Line
Demonstrates that the circumcenter, orthocenter, and centroid of a triangle all lie on a line called an Euler line. [6:12]
Khan Academy
Khan Academy: Geometry: Three Points Defining a Circle
Demonstates that any three non-collinear points can be used to define a unique triangle with a unique circumcenter and circumradius. These, in turn, define a unique circle. The center of the circle is the circumcenter of the triangle....
Khan Academy
Khan Academy: Algebra: Conic Sections: Three Points Defining a Circle
A video lesson that describes how any three non-collinear points actually define a circle. First it is shown that three points define a triangle. Then it is shown that the circumcenter of that triangle is actually the center of the...
Khan Academy
Khan Academy: Geometry: Circumcenter of a Right Triangle
Proves that the circumcenter of a right triangle is the midpoint of the hypotenuse. [5:42]
Khan Academy
Khan Academy: Geometry: Circumcenter of a Triangle
Explains using multiple proofs that a point on a perpendicular bisector is equidistant from the endpoints of the segment it bisects. Proofs use triangle congruency postulates. Lays the foundation for understanding the circumcenter of a...
Khan Academy
Khan Academy: Triangles: Euler Line
A video demonstration of the magic and mystery of the Euler Line.
Khan Academy
Khan Academy: Triangles: Review of Triangle Properties
Provides a review of perpendicular bisectors, angle bisectors, medians, and altitudes and the special points of concurrency formed by these parts of a triangle.
Khan Academy
Khan Academy: Triangles: Circumcenter of a Triangle
Multiple proofs showing that a point is on a perpendicular bisector of a segment if and only if it is equidistant from the endpoints. Using this to establish the circumcenter, circumradius, and circumcircle for a triangle.
Khan Academy
Khan Academy: Triangles: Circumcenter of a Right Triangle
The video tutorial shows that the midpoint of the hypotenuse is the circumcenter.
Khan Academy
Khan Academy: Geometry: Euler's Line Proof
Proves that the circumcenter, orthocenter, and centroid all lie on the same line, the Euler line. Proof relies on understanding of properties of similar triangles and properties of special parts of a triangle. [9:50]