Chord of a Circle
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A 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
chord circle center to midpoint distance Formula
\(\large{ h_c = r - h_s }\)
\(\large{ h_c = \sqrt{ r^2 - \frac{ c^2 }{ 4 } } }\)
Where:
\(\large{ h_c }\) = chord circle center to midpoint distance
\(\large{ l_c }\) = chord length
\(\large{ r }\) = circle radius
\(\large{ h_s }\) = segment height