Question

AB is a chord of a circle and AOC is its diameter such that angle ACB =50 degrees. If AT is the tangent to the circle at point A, then find angle BAT

Answer 1

answer is in the picture below...

Answer 2

The $\angle BAT$ = 50°.

Step-by-step explanation:

We are given that AB is a chord of a circle and AOC is its diameter such that  $\angle$ACB = 50°.

Also, AT is the tangent to the circle at point A.

As we can clearly see in the figure that $\triangle$ABC is a right-angled triangle with right angle at B. So, the sum of all angles of a triangle is equal to 180°.

In $\triangle$ABC ;

$\angle$ABC + $\angle$BAC + $\angle$ACB = 180°

90° + $\angle$BAC + 50° = 180°

140° + $\angle$BAC = 180°

$\angle$BAC = 180° - 140° = 40°.

Now, we are given that AT is the tangent to the circle at point A, this means;

$\angle$BAC + $\angle$BAT = 90°    {beacuse tangent is perpendicular to the radius}

40° + $\angle$BAT = 90°

$\angle$BAT = 90° - 40° = 50°.