Teorema Ptolemy pada Segi Empat Siklik

Abstract

Ptolemy's theorem, taken from the name of the Ancient Greek Philosopher Claudius Ptolemy (170 – 100 BC). Ptolemy's theorem is the relationship of 4 sides with 2 diagonals of Quadrilaterals in a circle. What is Quadrilateral? We have known Quadrilateral since elementary school. Square, rectangle, trapezoid, parallelogram, kite, rhombus are all Quadrilaterals. So Quadrilateral is a flat shape that has 4 sides. In Euclidean geometry, Ptolemy's theorem is the relationship between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on the same circle). This theorem is named after the Greek astronomer and mathematician, Ptolemy (Claudius Ptolemaeus). Ptolemy's theorem verbally can be stated as follows: "If a quadrilateral lies in a circle, the product of its diagonals is equal to the sum of the products of the pairs of opposite sides." In addition, the opposite of Ptolemy's theorem is also true, as follows: "In a quadrilateral, if the sum of the products of two pairs of opposite sides is equal to the product of the diagonals, then the quadrilateral can be described in a circle".