Question

figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If AOB = 100°,

then BAT is equal to

A) 100°
B)40°
C)50°
D)90°​

Answer 1

b)  50°

Explanation:

Given:  AO and BC are the radii of the circle

            since  AO = BO

∴  △AOB is an isosceles triangle

    Now,   in △AOB

  ∠AOB + ∠OBA +∠OAB = 180°                             [angle sum property]

    100° + ∠OAB + ∠OAB = 180 °

                          2 ∠OAB = 80°

                              ∠OAB = 40°

We know that the radius and tagent are perpendicular at their point of contact

∵             ∠OAT = 90°

 ∠OAB + ∠BAT = 90°

                ∠BAT = 90° - 40°

               ∠BAT = 50°

Therefore, ∠BAT is equaled to 50°