AB is the chord of the circle, and AOC is its diameter, such that ACB = 65º. If AT is the tangent to the circle at point A, then angle BAT is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 65º.
Given that
AB is the chord of the circle, and AOC is its diameter, such that ACB = 65º
AT is the tangent to the circle at point A
According to the question
As we know, Diameter makes a 90º angle on the circumference of the circle
∠ABC = 90º
⇒ ∠ABC + ∠ACB + ∠BAC = 180º
⇒ 90º + 65º + ∠BAC = 180º
∠BAC = 25º
and ∠CAT = 90º (Tangent on the circle)
∠BAT = ∠CAT - ∠BAC
= 90º - 25º = 65º