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

Lesson 4: Perpendicular bisectors

Proof of the formula relating the area of a triangle to its circumradius. Created by Sal Khan.

## Want to join the conversation?

• At around Sal says, "we've proven that an inscribed angle that is subtended by an arc will be half the arc length." When was this proven and how?
• What does "Subtend" mean?
• In most maths contexts subtend means CONNECTED TO but normally also on the OPPOSITE side of a figure. e.g. a third of a circle SUBTENDS an angle of 120 degrees at the centre of the circle. If you draw the arc of 1/3 of a circle and CONNECT each end of it to the centre you find the 120 degree angle between the 2 connecting radii. But the angle is kinda OPPOSITE the curve of the arc in that shape. I hope that helps. If so please vote.

Best regards,
Sheridan
• I am not clear how 2 different quantities are equated here...radius is linear while area is 2 dimensional..
• That's an interesting problem. The cool part is that when you multiply and divide everything, it comes out OK. So if we have a triangle with sides 3, 4, and 5 inches, the area would be 6 square inches (since it's a right triangle). So, you multiply it out: abc is 3" times 4" times 5" or 60 cubic inches. Divide 60 cubic inches by 4 to get 15 cubic inches. Divide 15 cubic inches by 6 square inches (the area) to get 2.5 inches! The extra units cancel each other out! Pretty amazing, I think.
• Is there somewhere I can find a list of all the proofs, postulates, axioms, and theorems, etc in Mathematics: Algebra, Geometry, Trignometry, etc?
• At , Sal says that any triangle inscribed in a circle where one of the triangle's sides is the diameter of the circle, it will be a right triangle.
What video was that proved in?
• This concept is proven in the video "Right Triangles Inscribed in Circles (Proof). We are asked to accept this concept as a leap of faith in this video, for it will be proven later.
• This video seems out of place. I'm trying to go through geometry in a linear way, as material is presented here. Doing this has for the most part felt like new concepts build on old, there are no mysterious unexplained parts of the videos, etc. This video is an exception. It uses words that I don't know in a way that suggests that I've missed something, and talks about proofs that I don't think I've been exposed to. I've never heard the word "subtan" for instance. Am I the only one having this problem? I'm doing a section called "perpendicular bisectors".
• I Dun understand some thing ,, isn't b the circumcenter of triangle ? So how in , You considered the b center of circle.and distance from b to B which is vertex of triangle is a radius ?! Please,I need an instant answer , u used this then in similarity to say c over 2R
• b represents the length of side AC. The circumcenter wasn't denoted by any letter, but R was used to represent the length from the circumcenter to a point on the circle such as B.
(1 vote)
• How can you prove that there will always be a "circum circle" for every triangle?