A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in the major segment.
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Step by Step Explanation:
- Look at the image below:
The chord AB has a length equal to the radius of the circle.
This means that ΔOAB is an equilateral triangle. (all the sides and angels are equal and each angle measure 60°)
So, ∠AOB = 60°.
- We know that the angle subtended by a chord at the center is twice the angle subtended by the chord at a point in the major segment.
Consider a point R on the major segment.
∠AOB = 2∠ARB.
Therefore, ∠ARB = 30°