Metric relationships

Metric relationships in circles describe how lengths such as radii, diameters, chords, tangents, and distances from the center are related. These relationships can be expressed using algebraic formulas and geometric properties.

Important properties

• The diameter $d$ of a circle is $d = 2r$, where $r$ is the radius.

• The perpendicular from the center of the circle to a chord bisects the chord.

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

• The tangent to a circle at a point is perpendicular to the radius at that point.

• If two chords intersect inside a circle, the products of the segments are equal: $AE \times EB = CE \times ED$.