Ptolemy's theorem
If ABCD is a cyclic quadrilateral, then the product of the two diagonals is equal to the sum of the products of opposite sides.
i.e AC x BD = (ABxCD) + (ADxBC)
- Theorem 1: If two chords AB and CD of a circle intersect at a point E inside the circle, then the product of the lengths of the segments AE and EB of the chord AB is equal to the product of the lengths of the segments CE and ED of the chord CD.
If A, B, C and D are any four points of a circle and if the line AC intersects the line BD at a point E, then
|AE| |EB| = |CE| .|ED|.
- Theorem: 2: If two secants are drawn to a circle from a point E outside of the circle, then the products of the length of the secant and the length of the external segment is the same for both secants.
|EA| |EB| = |EC| .|ED|
- Theorem 3: If a secant and tangent are drawn to a given circle from a point E outside of the circle, then the square of the of the length of the tangent segment is equal to the product of the secant and the length of its external segment.
|EA| |EB| = |EO| 2
