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what is formula for orthocentre of a triangle or how to calculate it?

what is formula for orthocentre of a triangle or how to calculate it?
 

Grade:11

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
7 years ago
Direct formula is there but it is not useful as it is in terms of tanA , tanB , tanC which is not useful
Easiest way to find orthocentre:

i) It is the point of concurrency of the 3 altitudes of the triangle.

ii) First find slope of any two sides; say AB & AC using slope formula. Then slope of the perpendicular to AB through C will be negative reciprocal of the slope of AB. Then using slope-point form, find the equation of the altitude through C.

iii) Similarly, equation to the altitude through B for the side AC can be found out.

iv) Then solve these two altitude equations, which would give the orthocentre of the triangle.

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