The chord of a circle is equal to its radius. Find the difference between the angle subtended by this chord at the minor arc and major arc of the circle.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 120°.
Let the chord be AB
The radius of the circle is equal to its chord
So,
⇒ AO = OB = AB
Thus, triangle AOB is an equilateral triangle
We know that an angle on the circle is always half of the angle made on the center
like ∠APB = 1/2 ∠AOB
So, ∠APB = 30°
And we know that the sum of the opposite angles of a cyclic quadrilateral is 180°
So, ∠AQB = 180° - 30° = 150°
Thus,
The difference between the major and minor arc = 150° - 30° = 120°