Question

In the figure below, O is the centre of the circle.

What is the diameter of the circle?

Answer 1

Given: O is the centre of the given circle.

As O is the centre of the circle, AC is the diametre of the given circle.

∠ABC is an angle in a semicircle.

We know that angle in a semicircle is a right angle.

∴ ∠ABC = 90°

Also, ∠CAB = 30°

Using angle sum property in ΔABC:

∠ABC + ∠BCA + ∠CAB = 180°

⇒ 90° + ∠BCA + 30° = 180°

⇒ 120° + ∠BCA = 180°

⇒ ∠BCA = 180° − 120° = 60°

Thus, the angles of ΔABC are 30°, 60° and 90°.

Therefore, the ratio of the lengths of the sides of ΔABC is 1::2.

_{AC = 2 × BC = 2 × 2.5 cm = 5 cm}

Therefore, the diametre of the given circle is 5 cm.