Question : AB is a chord of the circle and AOC is its diameter such that $\angle$ACB = 65°. If AT is the tangent to the circle at the point A, then $\angle$BAT is equal to:
Option 1: 65°
Option 2: 75°
Option 3: 55°
Option 4: 40°
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Correct Answer: 65°
Solution :
In a circle, the angle between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment.
Here, AB is the chord and AT is the tangent at point A.
So, the angle BAT is equal to the angle subtended by the chord AB at the alternate segment, which is angle ACB.
Given that $\angle$ACB = 65°, $\angle$BAT is also 65°.
Hence, the correct answer is 65°.
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