Geometry / 01

Power
of a point.

Two lines.
One equal product.

Turn the lines through P. Their lengths change, but the product stays the same.

Why it works

The invariant

Fixed P. Equal products.

PC × PD

OP² − r²

· lengths rounded

Two secantsFIG. 01

Drag P or A–D. Moving an endpoint turns its line through P.

Move point with arrow keys

The proof

Two secants, same product.