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## Geometry (all content)

### 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.
• 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?