"Concentric circle" division.

The ratio of radii of two concentric circles is 2:1.From a point P on the outer circle,a pair of tangents PA?

• The ratio of radii of two concentric circles is 2:1.From a point P on the outer circle,a pair of tangents PA and PB is drawn to the inner circle which meets inner circle at A and B.In triangle PAB,locate the centroid. (a) Inside the inner circle (b) On the inner circle (c) Outside (d) Depends on radii

• Answer:

  Take the radius of the smaller circle as the unit of length. If O is the centre of the circles, then triangle OAP has sides 1, sqrt(3), 2, and so it's a 30, 60, 90 (degrees) triangle. Hence triangle PAB is equilateral with sides sqrt(3), altitude 3/2. Its centroid is two thirds of the way down the altitude, i.e. 1 unit from P. Thus the correct answer is (b) On the inner circle.