# orthocenter of a triangle formula

The three altitudes of a triangle (or its extensions) intersect at a point called orthocenter.. Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. The orthocenter of a triangle is denoted by the letter 'O'. We know that, for a triangle with the circumcenter at the origin, the sum of the vertices coincides with the orthocenter. There is no direct formula to calculate the orthocenter of the triangle. CENTROID. It lies inside for an acute and outside for an obtuse triangle. The altitude can be inside the triangle, outside it, or even coincide with one of its sides, it depends on the type of triangle it is: . In this case, the orthocenter lies in the vertical pair of the obtuse angle: It's thus clear that it also falls outside the circumcircle. Find the slopes of the altitudes for those two sides. I found the equations of two altitudes of this variable triangle using point slope form of equation of a straight and then solved the two lines to get the orthocenter. Formula to find the equation of orthocenter of triangle = y-y1 = m (x-x1) y-3 = 3/11 (x-4) By solving the above, we get the equation 3x-11y = -21 ---------------------------1 Similarly, we have to find the equation of the lines BE and CF. The altitude of a triangle is a perpendicular segment from the vertex of the triangle to the opposite side. The slope of the line AD is the perpendicular slope of BC. The point where the altitudes of a triangle meet are known as the Orthocenter. It passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle. The orthocenter of a triangle is described as a point where the altitudes of triangle meet and altitude of a triangle is a line which passes through a vertex of the triangle and is perpendicular to the opposite side, therefore three altitudes possible, one from each vertex. The orthocentre point always lies inside the triangle. Slope of CF = -1/slope of AB = 2. (centroid or orthocenter) The three (possibly extended) altitudes intersect in a single point, called the orthocenter of the triangle, usually denoted by H. The orthocenter lies inside the triangle if and only if the triangle is acute (i.e. The point where the altitudes of a triangle meet is known as the Orthocenter. When the triangle is equilateral, the barycenter, orthocenter, circumcenter, and incenter coincide in the same interior point, which is at the same distance from the three vertices. (–2, –2) The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. The orthocenter of a triangle is the intersection of the triangle's three altitudes.It has several important properties and relations with other parts of the triangle, including its circumcenter, incenter, area, and more.. Triangle ABC is right-angled at the point A. Altitude. It is also the vertex of the right angle. If the triangle is There is no direct formula to calculate the orthocenter of the triangle. Slope of CA (m) = 3+6/4-3 = 9. The Euler line - an interesting fact It turns out that the orthocenter, centroid, and circumcenter of any triangle are collinear - that is, they always lie on the same straight line called the Euler line, named after its discoverer. We know that, for a triangle with the circumcenter at the origin, the sum of the vertices coincides with the orthocenter. Constructing the Orthocenter of a triangle Adjust the figure above and create a triangle where the orthocenter is outside the triangle. Slope of AD = -1/slope of BC = 3/11. 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