Question

O is the centreof the circle,∠ACO = 50°Find the measure of angle

Answer 1

Given :

• ∠ACO = 50°

To find :

• The value of x

According to the question,

⇒ CO = AO

Reason : Radius of circle

⇒ ∠ACO = ∠CAO = ∠COA = 50°

Reason : Radius are equal. So, its angle are also equal.

⇒ ∠BDC = 50°

Reason : Angle in the same segment.

∴ x = 50°

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Theorem 1 :

The angle subtended by an arc of a circle at the centre is doubled the angle subtended by it at any point on the remaining part of the circle.

Theorem 2 :

The angle in a semicircle is a right angle.

Theorem 3 :

Angles in the same segment of a circle are equal.

Theorem 4 :

The sum of either pair of the opposite angles of a cyclic quaderilateral is 180°.