Secant-Tangent Theorem
The secant-tangent theorem (also called chord-tangent theorem ) is a theorem of Euclidean geometry . It describes the relationship between lines formed by a tangent, a secant and the associated circle (see drawing).
Given is a circle with a secant and a tangent that intersect at a point outside the circle. If the points of intersection of the circle are designated as respectively and the point of contact of the tangent as , then the following applies:
This statement can also be formulated as a ratio equation:
The secant-tangent theorem describes a special case of the secant theorem in which the intersection points of the second secant and the circle coincide at one point. The propositions can be proven - similarly to the string proposition - with the help of similar triangles . All three sentences can be summarized with the help of the concept of potency or unified into a single statement.
literature
- Max Koecher , Aloys Krieg: level geometry . 2nd Edition. Springer-Verlag Berlin Heidelberg New York, 2000, ISBN 3-540-67643-0 , p. 148
- H. Schupp: Elementargeometrie , UTB Schöningh (1977), ISBN 3-506-99189-2 , p. 150
- Schülerduden - Mathematics I . Bibliographisches Institut & FA Brockhaus, 8th edition, Mannheim 2008, ISBN 978-3-411-04208-1 , pp. 415-417
Web links
- Circular sets - teaching materials from the University of Lüneburg
- Emese Vargyas, Ysette Weiss-Pidstrygach: Which areas is the set of tendons about? - Slides for a lecture
- Power of a Point Theorem on cut-the-knot.org