12-03-09 Circumradius of a triangle

Prove that the circum radius of a triangle is given by

R = abc/4Î”

where Î” is the area fo the triangle
and a,b,c are the sides

5 Answers

we know that are of a triangle = 1/2 AB X DC
=1/2 c (ACsinA)
=1/2bcsinA
= bc/2 x a/2R ( since a/sinA =2R)
= abc/4R

refer the figure

This was good.. But I want you to prove this too... I know it is easy but just for the sake of it

since a/sinA =2R

Basically I wanted the proof without any assumptions :)

if S is the center of the circumcircle and R the circumradius then in triangle BDC , rightangled at B with angle BDC= angle BAC =A

sinA= sin angle BDC= BC/DC =a/2R

hence a/sinA =2R

Awesome work amit :)

thanks bhaiya

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