CAT 2007 — QA Question 3
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 & solution
- A
Between 0 and 90
- B
Between 0 and 30
Between 0 and 60
- D
Between 0 and 75
- E
Between 0 and 45
P and Q do not lie within the intersection of the two circles.
So they lie on the circumferences or outside the circumferences.
Case 1: If they lie on the circumferences, then ΔAPQ forms an equilateral triangle.
So, m ∠AQP = 60°
Case 2: From the diagram, if they lie outside the circumferences,
m ∠AQ'P' < 60°
Also, m ∠AQP would be 0° if A, Q and P were collinear.
But as P and Q cut each other in two distinct points, A, Q and P cannot be collinear.
∴ m ∠AQP > 0°
∴ The value, m ∠AQP lies between 0° and 60°
Hence, option (c).