Question

heeeelppppp!!!what is the circumference of a circle that circumscribes a triangle with side lengths 3 4 and 5

Answer 1

Quite a few ways to go about it. The easiest may be to set your triangle up on a coordinate plane and give it some thought.



What do you suppose we can do with that?

Answer 2

i suppose 3 is the radius?

Answer 3

you don't happen to have a picture of it by any chance?

Answer 4

nope

Answer 5

Here is a picture

Answer 6

yeap I was thinking -> http://www.mathopenref.com/thalestheorem.html

Answer 7

I just drew you a picture. That is all that is needed for a drawing.

No, the radius is not 3. We must FIND the circumcenter. This is the intersection of the Perpendicular Bisectors. I put it on the coordiante axes in this way so that the perpendicular bisectors would be trivial to determine.

What is the equation of the horizontal and vertical perpendicular bisectors?

Answer 8

There is an important fact: the right angle (= 90 degrees) is an "inscribed angle" and equals ½ of its "intercepted arc"
that means its intercepted arc is 180º (½ of the circle)

Answer 9

well... if 5 is the longest side... then that gives the diameter and thus the radius and pretty much the circumference

anyhow @nabiladh tkhunny and phi are pointing out to -> http://www.mathopenref.com/thalestheorem.html

Answer 10

phi is pointing out a wonderful shortest way to do this, given a right triangle. Without a right triangle, this method is of no value. It is an eyeball problem, given that it is a right angle.

Constructing the perpendicular bisectors will solve all such problems.

Why don't you talk to us before we dump any more facts or demonstrations.

Answer 11

@tkhunny sorry i was busy living my life unlike ou behind a computer thanks bye!