In fig O is the center of the circle If angle cab = 50 find AOB and OAB
Answers
Answer:
Correct option is B)
AO and OB are radii of the circle.
side AO=BO so, ∠OAB=∠OBA [Isosceles triangle AOB]
Angle subtended by chord at the centre of a circle is double of the angle subtended at it's circumference.
Therefore ∠AOB=2∠ACB
∠AOB=100
∘
In triangle AOB
The sum of all three angle will be 180
∘
So, ∠AOB+∠OBA+∠OAB=180
∘
100
∘
+∠OBA+∠OAB=180
∘
100
∘
+2∠OAB=180
∘
[∠OAB=∠OBA]
∠OAB=
2
80
∘
∠OAB=40
∘
Therefore option B is the answer
Answer:
Hence, ∠AOB is 100° and ∠OAB is 40°.
Step-by-step explanation:
Step : 1 We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by the arc at any point on the circumference.
∠ AOB = 2 ∠ ACB
= 2 × 50 ° [Given]
∠ AOB = 100 °
...(i)
Step : 2 Let us consider the triangle Δ OAB.
OA = OB (Radii of a circle)
Thus, ∠ OAB = ∠ OBA
In Δ OAB, we have:
∠ AOB + ∠ OAB + ∠ OBA = 180 °
⇒ 100 ° + ∠ OAB + ∠ OAB = 180 °
⇒ 100 ° + 2 ∠ OAB = 180 °
⇒ 2 ∠ OAB = 180 ° – 100 ° = 80 °
⇒ ∠ OAB = 40 °
Hence, ∠ OAB = 40 °
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