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The orthocenter of a triangle, usually denoted by H, is the point where the three (possibly extended) altitudes intersect. [1] [2] The orthocenter lies inside the triangle if and only if the triangle is acute. For a right triangle, the orthocenter coincides with the vertex at the right angle. [2]
A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle. Figure 4. The center N of the nine-point circle bisects a segment from the orthocenter H to the circumcenter O (making the orthocenter a center of dilation to both circles): [6]: p.152
Center of the circle passing through the midpoint of each side, the foot of each altitude, and the midpoint between the orthocenter and each vertex. X 6: Symmedian point: K:: Intersection of the symmedians – the reflection of each median about the corresponding angle bisector. X 7: Gergonne point: G e
The hippocampal subfields are four subfields CA1, CA2, CA3, and CA4 that make up the structure of the hippocampus.Regions described in the hippocampus are the head, body, and tail, and other hippocampal subfields include the dentate gyrus, the presubiculum, and the subiculum.
Common nine-point circle, where N, O 4, A 4 are the nine-point center, circumcenter, and orthocenter respectively of the triangle formed from the other three orthocentric points A 1, A 2, A 3. The center of this common nine-point circle lies at the centroid of the four orthocentric points. The radius of the common nine-point circle is the ...
The process of drawing the altitude from a vertex to the foot is known as dropping the altitude at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one-half of the product of an altitude's length and its base's length (symbol b) equals the triangle's area: A = h b /2 ...
where A, B, C denote both the triangle's vertices and the angle measures at those vertices; H is the orthocenter (the intersection of the triangle's altitudes); D, E, F are the feet of the altitudes from vertices A, B, C respectively; R is the triangle's circumradius (the radius of its circumscribed circle); and a, b, c are the lengths of the triangle's sides opposite vertices A, B, C ...
In geometry, the orthocentroidal circle of a non-equilateral triangle is the circle that has the triangle's orthocenter and centroid at opposite ends of its diameter.This diameter also contains the triangle's nine-point center and is a subset of the Euler line, which also contains the circumcenter outside the orthocentroidal circle.