Multiple choice

AB is a chord to a circle and PAT is the tangent to the circle at point A. If ∠BAT = 75o and ∠BAC= 45o, C being a point on the circle then, ∠ABC is equal to-

  1. 75o

  2. 45o

  3. 60o

  4. 120o
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the alternate segment theorem, the angle between tangent and chord (∠BAT = 75°) equals the angle in the alternate segment (∠BCA). In triangle ABC, ∠BAC = 45°, so ∠ABC = 180° - 45° - 75° = 60°. The angle at the center is twice the angle at the circumference, so ∠APB = 90°, making PAT a tangent.

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