Dependences between segments in circum

author: Петя
viewed: 1956 times
Българска версия:

• Theorem 1: If АВ and CD are two chords that go trough point М, where point M is inwardly for a circumference k, then MA.MB = MC. MD.

• Theorem 2: If АВ and CD are two chords and their continueses pass trough point М, which is outwardly for a circumference k, then MA.MB = MC.MD.

• Theorem 3: If point М is outwardly for a circumference k and trough M passes tangent МТ to k and  sectional which intersect k in points А and B,then МА.МВ = МТ².

• Definition: If we have a circumference k (O;R) and a point М. The number ОМ² – R² is called exponent on the point М about the circumference k.

   From the definition follows that the exponent on M about k is:

• a positive number: if M is outwardly point about k

• a negative number: if М is inwardly point aboutе  k

• zero, if М lies over k.

            From theorem 3 follows that the exponent on the outwardly point М about the circumference is equal on the  tangent's square and this tangent is from  М to the circumference.

            From the formula ОМ² – R² follows that two points have the same exponent about a given circumference then and then only when they on the same length from the circumference's centre. Therefore geometrical place of points (which have the same exponent about the same circumference) is a circumference which is concentric on the given circumference.