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An inscribed angle in a semicircle is a right angle.

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...

The sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate.

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then area(DeltaABC)=1/2AB·CD=AB·DE, and ABFG can be squared by rectangle squaring. The general ...

The triangle transformation principle gives rules for transforming equations involving an incircle to equations about excircles.

For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...

The width of a box is the horizontal distance from side to side (usually defined to be greater than the depth, the horizontal distance from front to back).

There is only one point in front of a perspective drawing where its three mutually perpendicular vanishing points appear in mutually perpendicular directions, but such a ...

A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...

If a points A^', B^', and C^' are marked on each side of a triangle DeltaABC, one on each side (or on a side's extension), then the three Miquel circles (each through a ...