Geometry-8 (CAT-2007)

Two circle 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 with in the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?

(1)   Between 0 and 90

(2)   Between 0 and 30

(3)   Between 0 and 60

(4)   Between 0 and 75

(5)   Between 0 and 45

Solution follows here:

Solution:

The two extreme cases for this are:

Case-I:

The two circles touch each other with both the points A and B coinciding:

In this case, the points P,A,Q are collinear and hence ÐAQP = 0^0.

Case-II:

The two circles cut each other with each of the centres lying on the circumference of the

other circle:

In this case APQ is an equilateral triangle, as the sides PA = QA = PQ = radius of either circle

Hence, ÐAQP = 60⁰

For ÐAQP = 0⁰, they won’t intersect each other.

For 0⁰ <ÐAQP < 60⁰, the two points P and Q won’t fall within the intersection of the circles.

For ÐAQP ≥ 60⁰, the two points P and Q fall within the intersection of the circles.

Answer (3)