PT is a tangent at the point R on a circle with centre O. SQ is a diameter, which when produced meets the tangent PT at P. If ∠SPT = 32º, then what will be the measure of ∠QRP?
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 29°
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Understanding |
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Given: ∠SPT = 32° Tangent is always perpendicular to the radius. |
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Application |
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∠ORP = 90° [Tangent is always perpendicular to the radius] In triangle POR: ∠POR = 180 – (90 + 32) = 58° In triangle ORQ: OQ = OR (Radius) So, ∠OQR = ∠ORQ Hence, ∠ORQ = ½ × (180 – 58) = 61° So, ∠QPR = 90 – 61 = 29° |
