HEELP!Formula for ORTHOCENTRE and CIRCUMCENTRE in coordinate geometry???

Question

Could someone tell me the formula for finding the orthocentre and circumcentre with coordinate geometry?

I need it DESPERATELY! I was supposed to find it from some resource and cant find it ANYWHERE!!!!!

The 1st answer basically DEFINES orthocentre, circumcentre, centroid, incentre, etc.

I want to know the FORMULA for finding COORDINATES of the ORTHOCENTRE and CIRCUMCENTRE of a TRIANGLE in a plane.

Thanx!

Answer 1

You must be talking only about triangles, because they always have a circumcenter, and incenter, and an orthocenter.

The circumcenter of a triangle is found by finding the intersection of the perpendicular bisectors of two sides of the triangle. The orthocenter is found by finding the intersection of two altitudes of the triangle.

The circumradius is equal to abc/4A where a,b,c are sides of the triangle and A is the area of the triangle. From this you can easily find the circumcenter.

The ortocenter for an acute triangle lies within the triangle. For a right triangle, it is the vertex of the right angle. For an obtuse triangle, it lies outside the triangle.

If you are given the vertices of the triangle, you can easily find the orthocenter, circumcenter, incenter, and centroid.

The inradius is = A/s, where A is area and s is semiperimeter.