Search results
Results from the WOW.Com Content Network
The altitude from A (dashed line segment) intersects the extended base at D (a point outside the triangle). In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge opposite the apex.
In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors: A triangle's altitudes run from each vertex and meet the opposite side at a right angle. The point where the three altitudes meet is the orthocenter.
The extended sides of the orthic triangle meet the opposite extended sides of its reference triangle at three collinear points. [23] [24] [22] In any acute triangle, the inscribed triangle with the smallest perimeter is the orthic triangle. [25] This is the solution to Fagnano's problem, posed in 1775. [26] The sides of the orthic triangle are ...
The midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes). In 1822, Karl Feuerbach discovered that any triangle's nine-point circle is externally tangent to that triangle's three excircles and internally tangent to its incircle ...
The three perpendicular bisectors meet in a single point, the triangle's ... An altitude of a triangle is a straight line through a vertex and perpendicular to ...
The nine-point circle of a reference triangle is the circumcircle of both the reference triangle's medial triangle (with vertices at the midpoints of the sides of the reference triangle) and its orthic triangle (with vertices at the feet of the reference triangle's altitudes). [6]: p.153
For any interior point P, the sum of the lengths of the perpendiculars s + t + u equals the height of the equilateral triangle.. Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. [1]
A circle with radius d around a point inside the triangle will meet or intersect at least two sides of the triangle. The distance from any point on a side of the triangle to another side of the triangle is equal or less than a = ln ( 1 + 2 ) ≈ 0.881 {\displaystyle a=\ln \left(1+{\sqrt {2}}\right)\approx 0.881} , with equality only for the ...