The Law of Sines can be proven by showing that everytriangle can be circumscribed by one of these figures.
Families of these geometric figures that are orthogonal to one another are named for Apolloniusof Perga. These figures can be defined as the locus of points whose distance from a pair of pointsholds to a fixed ratio. Ptolemy's theorem relates the length of the sides of a quadrilateral inscribed inone of these figures. One of these that passes through the midpoints and feet of the altitudes of atriangle is known as the (*) nine-point one. The Law of Sines can be proven by showing that everytriangle can be circumscribed by one of these figures. These figures arise when cutting a cone with a planeparallel to the base, and they have zero eccentricity. For 10 points, name this shape whose circumference ispi times its diameter.
Families of these geometric figures that are orthogonal to one another are named for Apolloniusof Perga.
circles