Question

In the given figure, O is the centre of a circle
and AOC = 140°. Find ABC.​

Answer 1

Step-by-step explanation:

Given that ∠AOC=140

∘

∠ABC=

2

140

=70

∘

Because WKT angle made by a chord aa any point on the circle is half the angle made by it at the center

In △AOC

AO=CO=radius

⟹∠OAC=∠OCA

And

2∠OCA=180−∠AOC

⟹∠OCA=

2

40

=20=∠OAC

In △ABC

AB=BC

⟹∠BAC=∠BCA

And

2∠BAC=180−∠ABC

⟹∠BAC=55

∠OAB=∠CAB−∠CAO=55–20=35

∘