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Question
In the given figure, AB is a diameter of the circle with centre ‘O’. If ∠COB = 55⁰ then the value of x is:
Options
27.5°
55°
110°
125°
Solution
27.5°
Explanation:
∠CAB = `1/2` × ∠COB
The angle subtends at the circumference is half the angle subtend at the centre.
∠CAB = `1/2` × 55⁰
∠CAB = 27.5⁰
AO and CO are the radius of the same circle.
AO = CO
∴ ∠ACO = ∠CAO
∴ ∠CAB = ∠CAO = 27.5⁰
∴ x = ∠CAO = 27.5⁰
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