Question

a chord of circle is equal to the radius of circle. find angles substended by chird at a point om minor arc and also point on the major arc

Answer 1

In ΔOAB,
AB = OA = OB (radii)
Hence ΔOAB is an equilateral triangle
That is each angle of ΔOAB is 60°
∴ ∠AOB = 60°
∠AOB = 2∠ACB [Angle subtended by an arc of a circle at the centre is double the angle subtended by it on any part of the circle]
Hence ∠ACB = 30°
In cyclic quadrilateral ADBC
∠ADB + ∠ACB = 180° (Sum of opposite angles in cyclic quadrilateral is 180°)
⇒ ∠ADB = 180° − 30° = 150°
Therefore, angle subtended by the chord at a point on the major arc and the minor arc is 30° and 150° respectively
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Answer 2

Hi there!

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For solutions, Refer to the attached picture.
Regrets for handwriting _/\_

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Let's see some related topics :

⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.

⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.

⚫ Secant : A line intersecting a circle at any two points, is called secant.

⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.

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