The orthocentre of a triangle is a point intersection of altitudes.
i. Take the equations of any two sides of a triangle. find the eqnations the lines perpendicular to those lines and passing through the opposite vertices. solve these two equations we get orthocentre of the triangle.
ii. If angles A,B,C and vertices A (x1 , y1) B (x2 , y2) and C (x3 , y3) of a ΔABC are given then orthocentre of ΔABC is given by
iii. If any two lines out of three lines AB, BC, CA, are perpendicular, then orthocentre is the point of intersection of two perpendicular lines.
iv. The orthocentre of the triangle with verties (0,0), (x1 , y1 ) and (x2 , y2) is
v. The orthocentre (O), centroid (G) and circumcentre (C) of any triangle lie in a straight line and G divides the join of O and C in the Ratio 2 :1
vi. In an equilateral triangle,orthocentre, centroid, circumcentre and incentre coinside.
