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)

C_1 and C_2 , are the two concentric circles withradii r_1 and r_2, (r_1 lt r_2) . If the tangents drawnfrom any point of C_2 , to C_1 , meet again C_2 , at theends of its diameter, then

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 C_1 and C_2 are concentric circles of radius 1and 8/3 respectively having centre at (3,0) on the argand plane. If the complex number z satisfies the inequality log_(1/3)((|z-3|^2+2)/(11|z-3|-2))>1, then (a) z lies outside C_(1) but inside C_(2) (b) z line inside of both C_(1) and C_(2) (c) z line outside both C_(1) and C_(2) (d) none of these

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 Q lies inside C but outside E Q lies outside both Ca n dE P lies inside both C and E P lies inside C but outside E

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

State true or false. (a) A median of a triangle may lie outside the triangle. (b). The medians of a triangle meet at more than one points. (c) The centroid of a triangle always lies inside the triangle.

Let L_1 and L_2 be two lines intersecting at P If A_1,B_1,C_1 are points on L_1,A_2, B_2,C_2,D_2,E_2 are points on L_2 and if none of these coincides with P, then the number of triangles formed by these 8 points is

Let C_1 and C_2 be two circles whose equations are x^2+y^2-2x=0 and x^2+y^2+2x=0 and P(lambda, lambda) is a variable point . List 1 a) P lies inside C1 ​ but outside C2 ​ 2)P lies inside C2 ​ but outside C1 ​ c)P lies outside C1 ​ but outside C2 ​ d)P does not lie inside C2 ​ List 2 p)λ ϵ (−∞,−1)∪(0,∞) q)λ ϵ (−∞,−1)∪(1,∞) r)λ ϵ (−1,0) s)λ ϵ (0,1)

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 circle of C_2 . Tangents to C_1 , from any point on C_3 intersect C_2 , at P and Q . Find the angle between the tangents to C_2 at P and Q. Also identify the locus of the point of intersec- tion of tangents at P and Q .