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### Course: Geometry (all content)>Unit 4

Lesson 4: Perpendicular bisectors

# Circumcenter of a triangle

To prove that any point on the perpendicular bisector of a segment is equidistant from the endpoints, draw the segment and bisector, and note that the bisector creates two right triangles. By the definition of a perpendicular bisector, the hypotenuses of these triangles are congruent. Using the Pythagorean theorem, show that the two right triangles are congruent, and thus the point on the bisector is equidistant from the two endpoints. Other proofs are also included in the video. Created by Sal Khan.

## Want to join the conversation?

• If you are given 3 points, how would you figure out the circumcentre of that triangle. Example -a(5,1), b(-2,0), c(4,8).
• This might be of help.
Step 1: Graph the triangle.
Step 2: Find equations for two perpendicular bisectors.
Step 3: Find the intersection of the two equations.
• What is the RSH Postulate that Sal mentions at ?
• it's called Hypotenuse Leg Congruence by the math sites on google. it says that for Right Triangles only , if the hypotenuse and one corresponding leg are equal in both triangles, the triangles are congruent.

it sounds like a variation of Side-Side-Angle... which is normally NOT proof of congruence. but it's really a variation of Side-Side-Side since right triangles are subject to Pythagorean Theorem. we know that if it's a right triangle, and we know two of the sides, we can back into the third side by solving for a^2 + b^2 = c^2.

hope that helps. :D
• Is the RHS theorem the same as the HL theorem?
• Yes, but it's called the HL postulate. Not theorem (which is different)
• I'm having trouble knowing the difference between circumcenter, orthocenter, incenter, and a centroid??
• how does a triangle have a circumcenter?
• A circle can be defined by either one or three points, and each triangle has three vertices that act as points that define the triangle's circumcircle. Each circle must have a center, and the center of said circumcircle is the circumcenter of the triangle.
• the circumference of a triangle formed by the points (1,2,3),(3,-1,5),(4,0,-3) is;
• Is there a video explaining all the postulates of triangles (like ASA or AAS) and RSH, and other postulates in Euclidean geometry?
Thanks!
• What does bisect mean? So, what is a perpendicular bisector?
(1 vote)
• "Bisect" means to cut into two equal pieces. A perpendicular bisector not only cuts the line segment into two pieces but forms a right angle (90 degrees) with the original piece.