Multiple choice

In a circle with centre O, chords PR and QS meet at the point T, when produced, and PQ is a diameter. If ∠ROS=42∘, then the measure of ∠PTQ is

  1. 59∘

  2. 58∘

  3. 48∘

  4. 69∘
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a circle with diameter PQ, when chords PR and QS meet at T externally, angle PTQ equals half the sum of arcs intercepted by the angle. Given ∠ROS = 42°, the central angle subtended by chord RS is 42°. The angle PTQ is half the difference of 180° and 42°, which equals 69°. Alternatively, using cyclic quadrilateral properties: ∠PTQ = 90° - (∠ROS/2) = 90° - 21° = 69°. Option D is correct.

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