Question : The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is:
Option 1: $75^{\circ}$
Option 2: $60^{\circ}$
Option 3: $150^{\circ}$
Option 4: $120^{\circ}$

Question

Question : The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is:

Option 1: $75^{\circ}$

Option 2: $60^{\circ}$

Option 3: $150^{\circ}$

Option 4: $120^{\circ}$

Team Careers360 · Accepted Answer

Correct Answer: $150^{\circ}$

Solution :
Chord AB = Radius
In $ riangle$OAB,
OA = BO = Radius
⇒ $ riangle$OAB is an equilateral triangle.
⇒ $\angle$AOB = $60^{\circ}$
Since the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
⇒ $\angle$AOB = 2 × $\angle$ACB
⇒ $\angle$ACB = $\frac{60^{\circ}}{2}$ = $30^{\circ}$
Since ACBD is a cyclic quadrilateral and opposite angles of a cyclic quadrilateral are supplementary,
$\angle$ACB + $\angle$ADB = $180^{\circ}$
⇒ $\angle$ADB = $180^{\circ}- 30^{\circ}=150^{\circ}$
Hence, the correct answer is $150^{\circ}$.

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Question : The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is:Option 1: 75∘Option 2: 60∘Option 3: 150∘Option 4: 120∘

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Question : The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is:
Option 1: $75^{\circ}$
Option 2: $60^{\circ}$
Option 3: $150^{\circ}$
Option 4: $120^{\circ}$