If A, B, C are three points on a circle with centre O such that ∠AOB=90° and ∠BOC=120°, then ∠ABC=
A. 60°
B. 75°
C. 90°
D. 135°
Answers
Given: A, B, C are three points on a circle with centre O such that ∠AOB = 90° and ∠BOC = 120°.
To find : ∠ABC
Solution :
We have, ∠BOC = 120° and ∠AOB = 90°.
Reflex ∠AOC = 360° - (∠AOB + ∠BOC)
Reflex ∠AOC = 360° - (90° + 120°)
Reflex ∠AOC = 360° - 210°
Reflex ∠AOC = 150°
Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Reflex ∠AOC = 2∠ABC
150° = 2∠ABC
∠ABC = 150°/2
∠ABC = 75°
Hence, ∠ABC is 75°.
Among the given options option (B) 75° is correct.
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Answer:
Step-by-step explanation:
We have, ∠BOC = 120° and ∠AOB = 90°.
Reflex ∠AOC = 360° - (∠AOB + ∠BOC)
Reflex ∠AOC = 360° - (90° + 120°)
Reflex ∠AOC = 360° - 210°
Reflex ∠AOC = 150°
Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Reflex ∠AOC = 2∠ABC
150° = 2∠ABC
∠ABC = 150°/2
∠ABC = 75°