Question:
Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?
Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?
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Draw diagrams for extreme distances between centers to visualise angle limits.
Updated On: Mar 20, 2026
- Between 0 and 90
- Between 0 and 30
- Between 0 and 60
- Between 0 and 75
- Between 0 and 45
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The Correct Option is C
Solution and Explanation
Since both circles have the same radius and do not fully contain each other’s center, the distance between P and Q is between R and 2R. Geometry of intersecting equal circles shows that maximum possible angle AQP occurs when distance PQ = R (tangent through intersection region), giving 60°. Minimum is 0° when points coincide along diameter. Thus range is \( 0^\circ \) to \( 60^\circ \).
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