Question

In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB=50∘. If AT is the tangent to the circle at the point A, then ∠BAT is equal to:

Solution

The correct option is C In figure AOC is a diameter of the circle. We know that, diameter subtends an angle 90∘ at the circle.  So, ∠ABC=90∘ In △ABC,∠A+∠B+∠C=180∘     [Since, sum of all angles of a triangle is 180∘ ] ⇒ ∠A+90∘+50∘=180∘ ⇒ ∠A+140=180 ⇒ ∠A=180∘−140∘=40∘            ∠A or ∠OAB = 40∘ Now, AT is the tangent to the circle at point A. So, OA is perpendicular to AT ∴ ∠OAT=90∘ ⇒ ∠OAB+∠BAT=90∘ On putting ∠OAB=40∘, we get ⇒ ∠BAT=90∘−40∘=50∘ Hence, the value of ∠BAT is 50∘.

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