AB and AC are two tangents to a circle having centers at point X. What will be the measure of ∠BAC if ∠BXC = 125°?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 55°.
Given,
AB and AC are the tangents to a circle from an external point A.
X is the center of the circle
∠BXC = 125°
Since AB and AC are tangents to the circle from the same external point A, ∠BAC is formed at the external point.
We know,
Tangents drawn from an external point to a circle are equal in length
The angle between the tangents ∠BAC = 180 - ∠BXC.
According to the question;
⇒ ∠BAC = 180 - ∠BXC
⇒ ∠BAC = 180 - 125
⇒ ∠BAC = 55°