Question

given that AB and AC are tangets to the circle and AC=BC then <CAB in the given figure is equal to​

Answer 1

Answer:

In the given figure, AB and AC are tangents to the circle at B and C, respectively, and O is the centre of the circle, then x equals

285454

OC⊥DA ∴ ∠OCD=90

∘

In △OCD,∠ODC=180−∠OCD−∠DOC

∠ODC=180

∘

−(90

∘

+65

∘

)

∠ODC=180

∘

−155

∘

=25

∘

Also OB⊥AB, ∴ ∠OBA=90

∘

In △DBA,∠DAB=180

∘

−(∠BDA+∠DBA)

=180

∘

−(25

∘

+90

∘

)

=180

∘

−115

∘

=65

∘

∴ ∠OAB=

2

1

×∠CAB(or ∠DAB)=

2

1

×65

∘

=32.5

∘

(∴ Tangents are equally inclined to the line joining the external pt. and the centre of the circle)

In △OBA,X=180−∠OAB−∠OBA=180

∘

−(90

∘

+32.5

∘

)

X=180

∘

−122.5

∘

=57.5

∘