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?  Choose the correct choice from the following answers
A) Between 0 and 90  B) Between 0 and 30  C) Between 0 and 60  D) Between 0 and 75  E) Between 0 and 45
Explanation :   It says P&amp;Q falls outside the intersection area of the circle.   The maximum point where P&amp;Q can be in the circle is represented by the 2 small dashes P1 and Q1, when they can be on the circumference of the other circle.   Suppose P &amp; Q are on the circumference of the other circle. (Represented by P1 and Q1)   Then AP1 = r1 (Radius of 1st circle)   AQ1 = r2 (Radius of 2nd circle)   Also P1Q1 = r1 = r2 (As radius of both the circles are same)   So AP1 = AQ1 = P1Q1. Hence ∆AP1Q1 is equilateral, and ∠AQ1P1 = 600.   Suppose P1 and Q1 drift away from the circle, and are at the points P&amp;Q represented in the diagram. Then the value is definitely less than 600.   If P and Q are collinear with A, then the angle is 0(0).   So, the maximum value is 600, and minimum 0(0)   Answer : Between 0 and 60
<result>C</result>
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?