Answer:
Option C is correct.
Step-by-step explanation:
Given: measure of arc AC= 76°
To find: ∠BAC
Figure is attached.
Circle with center O
Measure of arc AC = 76°
⇒ ∠AOC = 76°
ΔAOC is an isosceles triangle because OC = OA are radius.
⇒ ∠OAC = ∠OCA (angles opposite to equal sides are equal)
In Δ AOC,
∠AOC + ∠OAC + ∠OCA = 180 (Angle sum property of triangle)
∠AOC + ∠OAC + ∠OAC = 180
76 + 2∠OAC = 180
2∠OAC = 104
∠OAC = 52°
AB is tangent to circle.
using result, which states that Radius and tangent are perpendicular at point of contact.
we get,
∠OAB = 90°
∠BAC + ∠OAC = 90
∠BAC + 52 = 90
∠BAC = 38°
Therefore, Option C is correct.
