C1 and C2 are two concentric circles, the radius of C2 being twice that of C1. From a point P on C2, tangents PA and PB are drawn to C1. Then the centroid of the triangle PAB (a) lies on C1 (b) lies outside C1 (c) lies inside C1 (d) may lie inside or outside C1 but never on C1

C_(1) and C_(2) are two concentrate circles, the radius of C_(2) being twice that of C_(1) . From a point P on C_(2) tangents PA and PB are drawn to C_(1) . Prove that the centroid of the DeltaPAB lies on C_(1)

From a point P outside a circle with centre at C, tangents PA and PB are drawn such that 1/(CA)^2+ 1/(PA)^2=1/16 , then the length of chord AB is

Let E be the ellipse (x^2)/9+(y^2)/4=1 and C be the circle x^2+y^2=9 . Let Pa n dQ be the points (1, 2) and (2, 1), respectively. Then (a) Q lies inside C but outside E (b) Q lies outside both Ca n dE (c) P lies inside both C and E (d) P lies inside C but outside E

Let C_1 and C_2 be two circles with C_2 lying inside C_1 circle C lying inside C_1 touches C_1 internally andexternally. Identify the locus of the centre of C

Let a,b,c be the sides of a triangle ABC, a=2c,cos(A-C)+cos B=1. then the value of C is

Consider three circles C_1, C_2 and C_3 such that C_2 is the director circle of C_1, and C_3 is the director circlé of C_2 . Tangents to C_1 , from any point on C_3 intersect C_2 , at P^2 and Q . Find the angle between the tangents to C_2^2 at P and Q. Also identify the locus of the point of intersec- tion of tangents at P and Q .

If C_1,C_2,a n dC_3 belong to a family of circles through the points (x_1,y_2)a n d(x_2, y_2) prove that the ratio of the length of the tangents from any point on C_1 to the circles C_2a n dC_3 is constant.

Let C_1, C_2, ,C_n be a sequence of concentric circle. The nth circle has the radius n and it has n openings. A points P starts travelling on the smallest circle C_1 and leaves it at an opening along the normal at the point of opening to reach the next circle C_2 . Then it moves on the second circle C_2 and leaves it likewise to reach the third circle C_3 and so on. Find the total number of different path in which the point can come out of nth circle.

Let C be incircle of A B Cdot If the tangents of lengths t_1,t_2a n dt_3 are drawn inside the given triangle parallel to sidese a , ba n dc , respectively, the (t_1)/a+(t_2)/b+(t_3)/c is equal to 0 (b) 1 (c) 2 (d) 3

If 1/a,1/b,1/c are in A.P and a,b -2c, are in G.P where a,b,c are non-zero then