Question

O is the centre of the circle AC is a diameter if angle ACB is equal to 50 degree then find the measure of angle BAC

Answer 1

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

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

As we can clearly see in the figure that 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 ABC ;

ABC + BAC + ACB = 180°

90° + BAC + 50° = 180°

140° + BAC = 180°

BAC = 180° - 140° = 40°.

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

BAC + BAT = 90° (beacuse tangent is perpendicular to the radius)

40° + BAT = 90°

BAT = 90° - 40° = 50°.