Tangent‑Secant Theorem (Power of a Point)

The tangent‑secant theorem states that for a point P outside a circle with centre O, the product of the lengths of the two segments of any secant through P equals the square of the length of the tangent from P to the circle (PA·PB = PC·PD = PT²). This relation is also called the power of a point.

In the simulation the circle and the external point P can be moved with the mouse, and the tangent PT and the two secants PAB and PCD are drawn automatically. Step buttons at the top let students advance through a geometric proof that uses similar triangles, highlighting the equal angles and the correspondence of sides.

By changing the position of P students see how the products PA·PB and PC·PD remain equal to PT², reinforcing the concept of similar triangles and the power‑of‑a‑point theorem, useful in geometry and algebra problems.