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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= _______.
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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°
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