finding coordinates of circumcentre of a triangle in terms of sine of vertexes.

gsn57iaf

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Aug 16, 2016
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Sir though I can find out coordinates of circumcentre by usual method but I am not able to prove the followings;
"
How to prove that coordinates of circumcentre of triangle ABC are given by
{(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)}."

Please guide me in solving this.
Thanks and regards.
GS Negi
 
Sir though I can find out coordinates of circumcentre by usual method but I am not able to prove the followings;
"
How to prove that coordinates of circumcentre of triangle ABC are given by
{(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)}."

Please guide me in solving this.
Thanks and regards.
GS Negi
"...though I can find out coordinates of circumcentre by usual method but I am not able to prove..."

What is that usual method? Please share your work with us.
 
Finding Cicumcentre of a triangle; Please see attachment.
 

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  • Circumcentre.pdf
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