CAT 2003 - Retake — QA Question 45
Tangents & SecantsEasy
In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If ∠ATC = 30° and ∠ACT = 50°, then the angle ∠BOA is:
Answer & solution
Correct answer: 100°
100°
- B
150°
- C
80°
- D
Cannot be determined
Solution
In ∆ACT,
∵ ∠ACT = 50° and ∠ATC = 30°,
∴ ∠CAT = 100°
Applying the Alternate Segment theorem,
∠ABC = 50°
Since ∠CAT is the external angle of ∆ABC, the sum of ∠ABC and ∠BCA is 100°,
∴ ∠BCA = 50°
∴ ∠BOA = 100°
Hence, option (a).