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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:
- Draw the figure using the given information.
- Find the measures of ∠CAT and ∠ABC with reasons.
- Whether ∠CAT and ∠ABC are congruent? Justify your answer.
Solution
∠CAT = ∠OAT = 90° ...(By tangent theorem)
∠ABC = 90° ...(Angle in a semi-circle is right angle)- ∠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.]
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