Question

in the given figure O is the centre of the circle. Arc ab= arc bc = arc CD. if angle oab= 48 .find angle aob
angle bod
angle obd.

Answer 1

Answer:

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Answer 2

∠ AOB = 84°

∠ BOD = 168°

∠ OBD = 6°

Step-by-step explanation:

See the attached diagram.

Since arc AB = arc BC = arc CD and they are the arcs of the same circle, so line AB = line BC = line CD.

Now, ∠ OAB = 48° {Given}

From the isosceles triangle Δ AOB, {Since AO = BO = radius}

∠ AOB = 180° - ∠ OAB - ∠ OBA = 180° - 48° - 48° = 84° (Answer)

Now, Δ AOB ≅ Δ BOC ≅ Δ COD {Since AB = BC = CD}

So, ∠ AOB = ∠ BOC = ∠ COD = 84°

Then, ∠ BOD = ∠ BOC + ∠ COD = 84° + 84° = 168° (Answer)

Now, Δ BOD is an isosceles triangle as OB = OD = Radius.

So, ∠ OBD = ∠ ODB = x (say)

Now, ∠ OBD + ∠ ODB + ∠ BOD = 180°

⇒ 2x + 168° = 180°

⇒ 2x = 12°

⇒ x = 6°

Therefore, ∠ OBD = 6° (Answer)