Metric relationships (other)

Besides the well-known metric relationships like the Power of a Point, there are other useful formulas involving lengths and distances in circle geometry. These include relationships involving chords, secants, tangents, and distances from points to the center or circumference.

Important properties

• The length of a chord at distance $d$ from the center of a circle of radius $r$ is $2\sqrt{r^2 - d^2}$.

• If two chords $AB$ and $CD$ intersect at $E$ inside the circle, then $AE \cdot EB = CE \cdot ED$.

• If two secants $PAB$ and $PCD$ are drawn from a point $P$ outside the circle, then $PA \cdot PB = PC \cdot PD$.

• If a tangent $PT$ and a secant $PAB$ are drawn from $P$ outside the circle, then $PT^2 = PA \cdot PB$.