orthocenter
point of concurrency of altitudes
The orthocenter is a point of concurrency in a triangle. It is the point where the altitudes of the triangle intersect. An altitude is a line segment that starts from a vertex of a triangle, perpendicular to the opposite side, and intersects that side.
To find the orthocenter of a triangle, you need to first find the equations of the three altitudes. This can be done using the slope formula and the point-slope formula. Once the equations of the three altitudes are found, you can solve for the point where they intersect, which will be the orthocenter.
It is important to note that not every triangle has an orthocenter. It is only present in acute and right triangles. In an obtuse triangle, the altitudes do not intersect inside the triangle, but rather outside of it.
The orthocenter has several properties. For one, it lies inside the triangle only if the triangle is acute. It also lies on the extended line of each altitude. Additionally, it is the intersection point of the three perpendicular bisectors of the sides of a triangle when the triangle is acute or right.
More Answers:
Mastering Circumference Calculation: the Basics of Measuring Circular ObjectsMastering Circle Measurements: the Importance of the Radius in Calculating Circumference and Area.
Circles in Mathematics: Definition, Formulas, and Applications