In an obtuse triangle, the vertices intersect the corresponding extended base sides but not the base sides themselves.
2.
An obtuse triangle has only one inscribed square, with a side coinciding with part of the triangle's longest side.
3.
However, while the orthocenter and the circumcenter are in an acute triangle's interior, they are exterior to an obtuse triangle.
4.
Hence, for an obtuse triangle with acute angles A and B ( and longest side " c " ), the enclosing-ball slimness factor is:
5.
The heptagonal triangle is the only obtuse triangle that is similar to its orthic triangle ( the equilateral triangle being the only acute one ).
6.
The median " m " " c " from the longest side is greater or less than the circumradius for an acute or obtuse triangle respectively:
7.
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.
8.
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.
9.
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.
10.
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.
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