Circle Theorems & Tangency Lab
Explore the fundamental theorems of circles through interactive diagrams. Investigate inscribed angles, intersecting chords, tangent properties, and the power of a point. Adjust parameters, record measurements, and verify each theorem experimentally.
Guided Experiment: Inscribed Angle Theorem
What relationship do you predict between an inscribed angle and the central angle that subtends the same arc?
Write your hypothesis in the Lab Report panel, then click Next.
Interactive Diagram
Controls
Measurements
Key Formula
Inscribed angle = ½ × central angle (both subtending the same arc)
Data Table
(0 rows)| # | Trial | Theorem | Central ∠(°) | Inscribed ∠(°) | Arc(°) | Chord Prod. | Tangent L |
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Reference Guide
Central & Inscribed Angles
An inscribed angle is always half the central angle that subtends the same arc.
All inscribed angles subtending the same arc are equal. When the arc is a semicircle (180°), the inscribed angle is exactly 90° (Thales' theorem).
Chord Theorems
When two chords intersect inside a circle, the products of their segments are equal.
The secant-secant angle from an external point equals half the difference of the intercepted arcs.
Tangent Properties
A tangent to a circle is perpendicular to the radius at the point of tangency. Two tangent segments from the same external point are always equal in length.
The tangent-chord angle equals half the intercepted arc.
Power of a Point
For any point P outside a circle, the product of distances along any secant is constant and equals the square of the tangent length.
This power is the same for every secant line through P, which is why it is called the "power" of the point with respect to the circle.