Interactive
Theorems
Master IGCSE Geometry through real-time kinematics. Drag vertices to dynamically prove laws of the Incenter, Circumcenter, and Orthocenter.
Trigonometric Laws
Equation 01
The Sine Rule
a / sin(A) = b / sin(B)
Utilized when presented with a "matching pair" (an angle and its corresponding opposite side). The ratio is continuous across all sides and equal to the diameter (2R) of the circumcircle.
Equation 02
The Cosine Rule
a² = b² + c² - 2bc · cos(A)
Applied to determine a third side given two sides and the included angle (SAS configuration), or extracting an angle when all three sides are known (SSS).
Equation 03
Area of a Triangle
Area = ½ · ab · sin(C)
A generalized formula for geometric area computation requiring only two sides and their included angle, bypassing the need for a perpendicular altitude.