Question

AB is a chord of a circle with centre O. AOC is diameter of circle, AT is a tangent at A.

Write answers of the following questions:

1. Draw the figure using the given information.
2. Find the measures of ∠CAT and ∠ABC with reasons.
3. Whether ∠CAT and ∠ABC are congruent? Justify your answer.

Answer 1

1. 
   
2. 
   
   ∠CAT = ∠OAT = 90°    ...(By tangent theorem)
   ∠ABC = 90°    ...(Angle in a semi-circle is right angle)
3. ∠CAT = ∠ABC
   ∠CAT ≅ ∠ABC    ...[∴ The angle between a tangent of a circle and a chord drawn from the point of contact is congruent to the angle inscribed in the arc opposite to the arc intercepted by that angle.]