Question

calculate the angle subtended by the chord at the point on the major arc if the radius and the chord of the circle are equal in length.​

Answer 1

Answer:

30°

Step-by-step explanation:

Refer the attachment for figure.

In figure, Ab is the chord, O is the centre and C is any point on the major arc AB.

Now, given that AO = BO = AB

So, the triangle ABO is equilateral triangle. Hence, all the angles would be equal to 60°

Hence, angle AOB = 60°

Now, we know that angle subtended by a chord on the centre is double of the angle subtended by it on any point of its circumference.

So, 2∠ACB = ∠AOB

⇒ 2∠ACB = 60°

⇒ ∠ACB = 30°

Hence, the angle subtended by the chord on a point on its major arc is 30°

Answer 2

Solution:-

Given:-

OA = OB = AB ( Radius = Chord).

Now,

In ∆ AOB,

All the Three Sides are Equal.

Hence, It's a Equilateral Triangle.

=> AOB = OAB = OBA = 60°

Note:-

Angle Substended at the Centre is Twice the Angle Substended at the Circumference.

Hence,

2 ∠ACB = ∠AOB

=> ∠ACB = 60°/2

=> ∠ACB = 30°.

Hence,

The Angle Substended by the Chord at the Point on the Major Arc if the Chord & the Radius is of equal length is equal to 30°.