Is there any formula to find the co-ordinate of the orthocentre, incenter and circumcentre of a triangle when the co-ordinate of all 3 vertices of the triangle are given.

Asked by yashjain | 6th Dec, 2012, 10:07: PM

Expert Answer:

let A,B,C the angles of the triangle
For orthocentre co-ordinates are:
((x1tanA+x2tanB+x3tanC)/(tanA+tanB+tanC),(y1tanA+y2tanB+y3tanC)/(tanA+tanB+tanC))
 
For incentre co-ordinates are:
((x1sinA+x2sinB+x3sinC)/(sinA+sinB+sinC),(y1sinA+y2sinB+y3sinC)/(sinA+sinB+sinC))
 
 
For circumcentre co-ordinates are:
((x1sin2A+x2sin2B+x3sin2C)/(sin2A+sin2B+sin2C),(y1sin2A+y2sin2B+y3sin2C)/(sin2A+sin2B+sin2C))

Answered by  | 7th Dec, 2012, 12:55: AM

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