. Find the value of angle BCA
AE is a tangent at the point C on a circle with centre O. DB is a diameter, which when produced meets the tangent AE at A . If ∠DAE = 28°, then the measure of ∠BCA will be
A. 62°
B. 59°
C. 28°
D. 31°
Best Answer
Correct Option Is: D
Solution -:
In ΔOAC
∠OAC = ∠DAE = 28° (given)
∠OCA = 90° (Tangent is perpendicular to the radius at the point of contact)
Therefore, ∠AOC = 180° – 28° – 90° = 62°
Now, in ΔOBC
OB = OC (radius of circle)
So, ∠OBC = ∠OCB = 
= 59°
Now, required ∠BCA = ∠OCA – ∠OCB = 90° – 59° = 31°
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