obtuse triangle sentence in Hindi
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- In an obtuse triangle, the vertices intersect the corresponding extended base sides but not the base sides themselves.
- An obtuse triangle has only one inscribed square, with a side coinciding with part of the triangle's longest side.
- However, while the orthocenter and the circumcenter are in an acute triangle's interior, they are exterior to an obtuse triangle.
- Hence, for an obtuse triangle with acute angles A and B ( and longest side " c " ), the enclosing-ball slimness factor is:
- The heptagonal triangle is the only obtuse triangle that is similar to its orthic triangle ( the equilateral triangle being the only acute one ).
- The median " m " " c " from the longest side is greater or less than the circumradius for an acute or obtuse triangle respectively:
- The smallest containing circle for an acute triangle is its circumcircle, while for an obtuse triangle it is the circle having the triangle's longest side as a diameter.
- In an obtuse triangle the two shortest sides'perpendicular bisectors ( extended beyond their opposite triangle sides to the circumcenter ) are divided by their respective intersecting triangle sides in equal proportions.
- This is illustrated in the adjacent diagram : in this obtuse triangle, an altitude dropped perpendicularly from the top vertex, which has an acute angle, intersects the extended horizontal side outside the triangle.
- For example, you cannot draw a completely general triangle, as the specific triangle in your diagram will be either a right triangle, an acute triangle or an obtuse triangle-it cannot be all three at the same time.
- Likewise, a triangle's circumcenter & mdash; the intersection of the three sides'perpendicular bisectors, which is the center of the circle that passes through all three vertices & mdash; falls inside an acute triangle but outside an obtuse triangle.
- Among oblique pyramids, like acute and obtuse triangles, a pyramid can be called " acute " if its apex is above the interior of the base and " obtuse " if its apex is above the exterior of the base.
- Even if a polygon has a circumscribed circle, it may not coincide with its minimum bounding circle; for example, for an obtuse triangle, the minimum bounding circle has the longest side as diameter and does not pass through the opposite vertex.
- For an acute triangle, six of the points ( the midpoints and altitude feet ) lie on the triangle itself; for an obtuse triangle two of the altitudes have feet outside the triangle, but these feet still belong to the nine-point circle.
- In an obtuse triangle ( one with an obtuse angle ), the foot of the altitude to the obtuse-angled vertex falls on the opposite side, but the feet of the altitudes to the acute-angled vertices fall on the opposite extended side, exterior to the triangle.
- The smallest possible ratio of the side of one inscribed square to the side of another in the same non-obtuse triangle is 2 \ sqrt { 2 } / 3 = 0.94 . . . . Both of these extreme cases occur for the isosceles right triangle.
- As a result, in an isosceles triangle with one or two angles of 36? the longer of the two side lengths is " ? " times that of the shorter of the two, both in the case of the acute as in the case of the obtuse triangle.
- In these cases the vertex figure is highly distorted to achieve uniformity with flat faces : in the first two cases it is an obtuse triangle instead of an acute triangle, and in the last three it is a pentagram or hexagram instead of a pentagon or hexagon, winding around the centre twice.
- Since barycentric coordinates are all positive for a point in a triangle's interior but at least one is negative for a point in the exterior, and two of the barycentric coordinates are zero for a vertex point, the barycentric coordinates given for the orthocenter show that the orthocenter is in an acute triangle's interior, on the right-angled vertex of a right triangle, and exterior to an obtuse triangle.
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