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Mathematics

The Inscribed Angle Theorem and Its Generalizations for Circles

Quick fact

The inscribed angle theorem tells us that any angle inscribed in a circle is exactly half the measure of its intercepted arc. This means that if two inscribed angles intercept the same arc, they are always equal, regardless of where their vertices are on the circle.

Why this is interesting

Picture a circle with a fixed arc, and imagine standing at different points on the circle looking at that arc. The angle you see never changes—no matter where you stand on the circle. Why?