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The following applications may take some time to load depending on connection speed. Please wait. CIRCUMSCRIBED CIRCLE- A triangle is said to be inscribed in a circle that contains all of its vertices and the circle is said to be circumscribed about the polygon. The circle is called the circumcircle of the polygon and its center is called the circumcenter of the polygon.
- The perpendicular bisectors of the sides of the triangle are concurrent and the point of the concurrency is the circumcenter.
- Every triangle is cyclic. (A polygon is cyclic if there exists a circle that contains all of its vertices)
INSCRIBED CIRCLE- A circle is inscribed in a triangle if each side of the triangle is tangent to the circle.
- The circle is called the incircle of the triangle. Its center is called the incenter of the triangle.
- Every triangle has an incircle.
The angle bisectors of a triangle are concurrent and the point of concurrency is the incenter of the triangle.Excircles (Escribed Circles)Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an excircle, or sometimes an escribed circle.The center of the excircle is called the excenter and lies on the external angle bisector of the opposite angle.Every triangle has three excircles.You can investigate the applications by moving the empty squared points.
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Solids