Power of a Point

A product that never changes

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• For any line through $P$ meeting the circle at $A$ and $B$, $PA \times PB$ is constant.
• It equals the tangent length squared: $PT^2 = d^2 - r^2$.
• Distance to the horizon: $d \approx \sqrt{2Rh}$.

Steps

1. Secants from a point
2. Tangent from secant
3. Crossing chords
4. Power at the centre
5. Inside the circle
6. How far is the horizon?