. 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 -:

circle

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 = circle = 59°

Now, required ∠BCA = ∠OCA – ∠OCB = 90° – 59° = 31°

 

Talk to Our counsellor