1
Question
O is the centre of the circle and BCD is the tangent to it at C.
Then, ∠BAC+∠ACD= _______.
O is the centre of the circle and BCD is the tangent to it at C.
Then, ∠BAC+∠ACD= _______.
Open in App
Solution
The correct option is B 90°
Consider △OCA,∠OCA=∠OAC
[Angles opposite to equal sides (OC = OA= radius) are equal ]
And,
OC⊥BD
[Tangent to a circle is always perpendicular to the radius at that point ]
From the figure, we know that,
∠OCA+∠ACD=90∘
Since
∠OCA=∠OAC
So,
∠OAC+∠ACD=90∘⇒∠BAC+∠ACD=90°
Consider △OCA,∠OCA=∠OAC
[Angles opposite to equal sides (OC = OA= radius) are equal ]
And,
OC⊥BD
[Tangent to a circle is always perpendicular to the radius at that point ]
From the figure, we know that,
∠OCA+∠ACD=90∘
Since
∠OCA=∠OAC
So,
∠OAC+∠ACD=90∘⇒∠BAC+∠ACD=90°
Suggest Corrections
0
Similar questions
In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
