Intersecting Chord Properties Both Internally and Externally
A chord AB of...
A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .
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AB = OA = OB = radius ∴ΔOAB is an equilateral triangle.
Therefore, each interior angle of this triangle will be of 60∘. ⇒∠AOB=60∘. ∠ACB=12∠AOB=12(60∘)=30∘
In cyclic quadrilateral ACBD, ∠ACB+∠ADB=180∘ (Opposite angle in cyclic quadrilateral are supplementary) ∴∠ADB=180∘−30∘=150∘
Therefore, angle subtended by this chord at a point on the major arc and the minor arc are 30∘ and 150∘ respectively.