Question

If the vertices of ∆ABC are A(cosa, sina),
B(cosß, sinß) and C(cosy, siny),
then the orthocentre of the triangle is​

Answer 1

Answer:

First, if you’re trying to give the coordinates of points then the values should be in parentheses, e.g. (cos x, sin x), not square brackets.

Second, I’m not sure why you gave the coordinates as trigonometric functions other than it being an obscure way of saying that the vertices all have to be on a unit circle. Other than that, the method here is going to be the same as it would be if you just chose three random points:

Find the equation of the slope of the line through AB.

Find the equation of the line perpendicular to AB that passes through C. (Remember that the slopes of perpendicular lines are negative reciprocals of each other.) This gives you the equation of one of the triangle’s altitudes.

Find the equation of the slope of the line through BC.

Find the equation of the line perpendicular to BC that passes through A. This gives you the equation of a second altitude.

Find the location of the intersection of the lines from (2) and (4) and you’ll have the location of the orthocenter.

My choice of sides AB and BC was arbitrary. You can use any two sides and you should get the same result.

Explanation: