Question
Download Solution PDFIf 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
PQ is a tangent to the circle, touching it at point Q.
O is the centre of the circle.
∠POQ = 75°
Concept Used:
The tangent at any point makes an angle of 90° with the radius drawn to the point of tangency.
The sum of the angles in a triangle equals 180°.
Calculation:
The tangent at any point makes an angle of 90° with the radius.
Therefore, ∠OQP = 90° (since OQ is the radius and PQ is the tangent at Q).
We need to find the value of ∠OPQ.
However, we know that the sum of the angles in a triangle equals 180°.
So, we have ∠OPQ + ∠OQP + ∠POQ = 180°.
Substituting the given values into the equation, we get:
∠OPQ + 90° + 75° = 180°
∠OPQ = 180° - 90° - 75°
∠OPQ = 15°
So, the value of ∠OPQ is 15°.
Last updated on Jun 26, 2025
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