Sine of an Angle in a Cyclic Quadrilateral with Given Area Ratio

This GeoGebra example illustrates a cyclic quadrilateral ABCD inscribed in a circle where AB is the diameter. A point P is introduced such that the area ratio of triangle PCD to quadrilateral ABCD is 1:8, and the goal is to determine sinθ. The construction leverages key geometric properties: angles subtended by a diameter are right angles, area relationships in cyclic figures, and trigonometric definitions. Built using GeoGebra commands including Circle, Semicircle, Point, Polygon, Line, OrthogonalLine, Segment, and Angle, the model dynamically links geometry and trigonometry. It is ideal for high school students studying advanced Euclidean geometry, trigonometric applications, or preparing for mathematical competitions involving circle theorems and area ratios.