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?

Accepted Answer

C. In $	riangle APQ$, $AP = AQ = r$. So $	riangle APQ$ is isosceles. Since P and Q lie outside the intersection, the distance $PQ$ ranges between $r$ and $2r$. When $PQ = r$, $	riangle APQ$ is equilateral and $\angle AQP = 60^\circ$. As $PQ 	o 2r$, $\angle AQP 	o 0^\circ$. So angle AQP ranges between $0^\circ$ and $60^\circ$.

Smallest range of angle between intersecting circles

Explanation

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