Chord of a Circle

Written by Jerry Ratzlaff on . Posted in Geometry

  •  circle 12circle 10A line segment on the interior of a circle.
  • An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.

Chord Angle of a Circle Formula

\(\large{ m\theta_{1} =  \frac{1}{2} \; \left( m\overset{\frown}{AC} + m\overset{\frown}{EG} \right) }\)

\(\large{ m\theta_{2} =  \frac{1}{2} \; \left( m\overset{\frown}{CE} + m\overset{\frown}{GA} \right) }\)

\(\large{ m\theta_{1} = m\theta_{3} }\)

\(\large{ m\theta_{2} = m\theta_{4} }\)

Where:

\(\large{ \theta }\) = angle

\(\large{ \frown }\) = chord arc length

Chord Arc Length of a Circle Formula

\(\large{ l =  \frac { \theta} { 180 } \; 2 \; \pi \;  r }\)

Where:

\(\large{ l }\) = length

\(\large{ r }\) = radius

\(\large{ \theta }\) = angle

\(\large{ \pi }\) = Pi

Chord Length of a Circle formula

\(\large{ c = 2 \; r \; \sin \; \frac {\theta}{2}  }\)

\(\large{ c = 2 \; \sqrt{r^2-h^2}  }\)

Where:

\(\large{ c }\) = chord

\(\large{ h, h' }\) = height

\(\large{ r }\) = radius

\(\large{ \theta }\) = angle

Chord Tangent of a Circle Formula

\(\large{ m\theta_{1} =  \frac{1}{2} \; \left( m\overset{\frown}{ABC} \right) }\)

\(\large{ m\theta_{2} =  \frac{1}{2} \; \left( m\overset{\frown}{EAZ} \right) }\)

\(\large{ m\theta_{3} =  \frac{1}{2} \; \left( m\overset{\frown}{GAB} \right) }\)

Where:

\(\large{ \theta }\) = angle

\(\large{ \frown }\) = chord arc length