cyclic polygon造句

• Note that this theorem is easily extended to prove the Japanese theorem for cyclic polygons.
• After proving the quadrilateral case, the general case of the cyclic polygon theorem is an immediate corollary.
• A cyclic polygon has each of its vertices on a particular circle, called the circumcircle or circumscribed circle.
• Thus if " n " is odd, a cyclic polygon is equiangular if and only if it is regular.
• A polygon inscribed in a circle is said to be a cyclic polygon, and the circle is said to be its circumscribed circle or circumcircle.
• In a cyclic polygon, longer sides correspond to larger exterior angles in the dual ( a tangential polygon ), and shorter sides to smaller angles.
• In the proof, both the Japanese theorem for cyclic quadrilaterals and the quadrilateral case of the cyclic polygon theorem are proven as a consequence of Th閎ault's problem III.
• A polygon which has a circumscribed circle is called a "'cyclic polygon "'( sometimes a "'concyclic polygon "', because the vertices are concyclic ).
• With the additional construction of a parallelogram having sides parallel to the diagonals, and tangent to the corners of the rectangle of incenters, the quadrilateral case of the cyclic polygon theorem can be proved in a few steps.
• A cyclic polygon is equiangular if and only if the alternate sides are equal ( that is, sides 1, 3, 5, . . . are equal and sides 2, 4, . . . are equal ).
• The midpoint-stretching polygon of a cyclic polygon ( a polygon whose vertices all fall on the same circle ) is another cyclic polygon inscribed in the same circle, the polygon whose vertices are the midpoints of the circular arcs between the vertices of.
• The midpoint-stretching polygon of a cyclic polygon ( a polygon whose vertices all fall on the same circle ) is another cyclic polygon inscribed in the same circle, the polygon whose vertices are the midpoints of the circular arcs between the vertices of.
• The quadrilateral rule can be applied to quadrilateral components of a general partition of a cyclic polygon, and repeated application of the rule, which " flips " one diagonal, will generate all the possible partitions from any given partition, with each " flip " preserving the sum of the inradii.