Interactive demonstrations of inscribed angles, tangent theorems, chord properties, and cyclic quadrilaterals with draggable points.
Circle Theorems Explorer turns inscribed-angle, tangent, chord, and cyclic-quadrilateral statements into movable circle diagrams. Drag the marked points to change the figure while observing the relationship associated with the selected theorem. It is especially useful for identifying which angle, chord, or arc a theorem concerns before attempting a proof. The common trap is following a point label but not its intercepted arc: when points change order around the circle, the relevant minor or major arc, and sometimes the intended angle, can change.
Each demonstration assigns geometric roles to its marked objects, such as a point on the circumference, a chord endpoint, a tangent contact, or a cyclic-quadrilateral vertex. Moving an available point updates the construction. This lets you inspect one theorem across many nondegenerate positions instead of relying on a single carefully arranged textbook drawing.
For an inscribed-angle configuration, compare the angle at the circumference with its intercepted arc or corresponding central angle. In a tangent configuration, identify the contact point and the relevant chord before comparing angles. For a cyclic quadrilateral, pair opposite rather than adjacent angles. The important observation is the relationship preserved during movement, not one convenient-looking shape.
Circle angles depend on the two rays forming the angle and on the arc they intercept. Passing another marked point can change which arc lies opposite the angle, or can turn a convex cyclic quadrilateral into a crossed configuration. Re-establish the order of the points and identify the relevant arc before treating the new value as a continuation of the previous case.
No. Dragging can test many examples and reveal a mistaken choice of angle, chord, or arc, but it cannot cover every permitted configuration. Treat the preserved relationship as evidence and as a guide to the theorem's hypotheses. A proof still requires a general argument, often using radii, isosceles triangles, central angles, or angle sums.
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