Find a chord from its inscribed angle and circle radius
A chord is twice the radius times the sine
For a chord seen from an inscribed angle θ on the opposite arc, its length is 2Rsin(θ). The same result follows from the extended sine rule in the inscribed triangle.
Problem
A circle has radius 37. Find the length of a chord subtended by an inscribed angle of 30 degrees.
Answer
The chord has length 37.
The angle is inscribed, not central; a central angle of 30 degrees would give a different chord.
Step-by-step solution
1. Connect the angle to its chord
In a triangle inscribed in a circle of radius R, the side opposite an angle θ has length 2Rsin(θ). The requested chord is that opposite side.
2. Substitute the measurements
With R=37 and θ=30∘, the chord length is 2(37)sin(30∘)=74(1/2)=37.
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