Question : If PQ is a tangent of a circle (touches the circle at Q ) with centre O and angle POQ is 75°, then what is the value of angle OPQ?
Option 1: 15°
Option 2: 35°
Option 3: 30°
Option 4: 25°
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Correct Answer: 15°
Solution :
In a circle, the radius is perpendicular to the tangent at the point of tangency. This means the angle between the radius (OQ) and the tangent (PQ) is 90°.
Given that the $\angle$POQ is 75°,
$\angle$OPQ = 180° – 90° – 75° = 15°
Hence, the correct answer is 15°.
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