Question

9. In the given figure, if O is the centre of circle. Chord AB is equal to radius of the circle, then find angle ACB.​

Answer 1

In the given figure OA and OB are the radii of the circle

OA =OB =AB ( given )

triangle OAB is an equilateral triangle

angle AOB =angle OAB = angle OBA = 60°

the measure of an angle subtended by an arc at a point on the circle is half of the measure of the angle subtended by the arc at the centre

angle ACB =1/2 angel AOB

1/2×60°

=30°

therefore angle ACB =30°

Answer 2

Answer:

Angle ACB = 30°

Step-by-step explanation:

As given in question that chord AB is equal to the radius of the circle.

OA=OB=AB

Therefore ΔAOB is an equilateral triangle.

∠OAB+∠AOB+∠OBA=180° (Angle Sum Property of Δ)

∠OAB=∠AOB=∠OBA=60°

Theorem 10.8 states that angle subtended by an arc at the centre of a circle is double than that of any angle formed at the remaining part of the circle.

Using this theorem,

∠AOC=1/2 ∠AOB

∠AOC= 60/2

∠AOC=30°