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

Question

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 1

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.

Answer 2

b) on the inner circle

Triangle PAB is an equilateral triangle.

Answer 3

a