Question

Given a circle with center O. AB is a chord and ∠ACB = 650
Find the value of x.
the final ans is given, can i pls know how

Answer 1

Answer:

we know that the angle subtended by the chord at the centre of the circle is double the angle subtended by it at any other point of the circle

therefore by above statement,

angle AOB = 2×angle ACB

angle AOB = 2×65

= 130⁰

Now, In triangle AOB,

AO = BO ( radius of the same circle )

let AO = BO = x

then using angle sum property of triangle ,

x+x+130=180

2x+130=180

2x =180-130

2x =50.

x=50/2

x=X=25⁰