Question

ABC is a triangle such that

BC * AD * AB = 200 cm^3
The area of the triangle is 40 cm^2 then the radius of the circle passing through it's heads is ... cm

Answer 1

what is AD?

Answer 2

AC sorry typo

Answer 3

circle passing through it's heads

does this passing through the vertices A,B, and C ?

Answer 4

it sounds hard.

Answer 5

any hints? what are you studying ?

Answer 6

5 hours thinking and no result :(
The question is in general questions , I also don't know the lesson name.

Answer 7

general questions?

Answer 8

I forgot
The question was in determinators
although I don't know what's the relation.

Answer 9

The picture = 200 cm^3

Answer 10

wikipedia says
diameter of the circumcircle = abc/2*area

so the radius is abc/area

Answer 11

how do you find the area?

Answer 12

It's given , but what is abc ?

Answer 13

of course silly me
abc = 200

Answer 14

a, b and c are the 3 sides of the traingle

Answer 15

200/40 = 5 ?
the book says the final answer is 5/4

Answer 16

os that correct for the radius @phi ?

Answer 17

I was looking at this
https://en.wikipedia.org/wiki/Circumscribed_circle

Answer 18

is 5/4 logical ?

Answer 19

yes I think it is
radius = abc / (4*area)

Answer 20

oops! what's a multiple of 2 one way or the other!

Answer 21

diameter of the circumcircle = abc/2*area
so radius is abc/4*area

Answer 22

yea lol

Answer 23

Yeah.

Answer 24

Thanks so much guys.

Answer 25

yw

Answer 26

but it's not obvious why it works

Answer 27

Where can I find how did they prove it ?

Answer 28

yea it's quite obscure

Answer 29

I would google.

Answer 30

https://www.khanacademy.org/math/geometry/triangle-properties/perpendicular_bisectors/v/area-circumradius-formula-proof
How about this ?

Answer 31

looks promising

Answer 32

yea