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The intersecting chords theorem or just chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords in a circle .. It states that the products of the lengths of the line segments on each chord are equal .. More precisely for two chords AC and BD intersecting in a point S the following equation holds  :. The converse is true as well , that is if for two line segments AC and BD intersecting in S the equation above holds , then their four endpoints A , B , C and D lie on a common circle .. Or in other words if the diagonals of a quadrilateral ABCD intersect in S and fulfill the equation above then it is a cyclic quadrilateral .. cyclic quadrilateral. cyclic quadrilateral. The theorem can be proven using similar triangles .. Consider the angles of the triangles ASD and BSC  :. This means the triangles ASD and BSC are similar and therefore. Next to the tangent-secant theorem and the intersecting secants theorem the intersecting chord theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle - the power of point theorem .. tangent-secant theorem. tangent-secant theorem. intersecting secants theorem. intersecting secants theorem. power of point theorem. Power of a point#Theorems