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?

Answer 1

Step-by-step explanation:

Let R be the radius of both the circles.

Maximum value for angle AQP is when the circles are close as shown in diagram 2 where PQ = AP = AP = R. (when P and Q are at the intersection). Since all sides are equal, triangle APQ is an equilateral triangle with each angle = 60°.

As per the question, P nor Q cannot fall within the intersection of the circles. Therefore, angle AQP < 60°

As the horizontal distance between the circles increases (as shown in diagram 1), value of angle AQP decreases. therefore angle AQP > 0°

This means angle AQP is between 0 and 60. Option c is the correct answer.