In the circle given below, let OA = 1 unit, OB = 13 unit and PQ $$\perp$$ OB. Then, the area of the triangle PQB (in square units) is :

Let A(1, 4) and B(1, $$-$$5) be two points. Let P be a point on the circle (x $$-$$ 1)2 + (y $$-$$ 1)2 = 1 such that (PA)2 + (PB)2 have maximum value, then the points, P, A and B lie on :

If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of radius r, then r is equal to :

Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2$$\sqrt{2}$$ and 2$$\sqrt{5}$$, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to :

The line 2x $$-$$ y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x $$-$$ 2y = 4. Then, the radius of the circle is :

Choose the incorrect statement about the two circles whose equations are given below : x2 + y2 $$-$$ 10x $$-$$ 10y + 41 = 0 and x2 + y2 $$-$$ 16x $$-$$ 10y + 80 = 0

Let the tangent to the circle x2 + y2 = 25 at the point R(3, 4) meet x-axis and y-axis at points P and Q, respectively. If r is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ, then r2 is equal to :

Two tangents are drawn from a point P to the circle x2 + y2 $$-$$ 2x $$-$$ 4y + 4 = 0, such that the angle between these tangents is {\tan ^{ - 1}}\left( {{{12} \over 5}} \right), where {\tan ^{ - 1}}\left( {{{12} \over 5}} \right) $$\in$$(0, $$\pi$$). If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of $$\Delta$$PAB and $$\Delta$$CAB is :

Choose the correct statement about two circles whose equations are given below : x2 + y2 $$-$$ 10x $$-$$ 10y + 41 = 0 x2 + y2 $$-$$ 22x $$-$$ 10y + 137 = 0

For the four circles M, N, O and P, following four equations are given : Circle M : x2 + y2 = 1 Circle N : x2 + y2 $$-$$ 2x = 0 Circle O : x2 + y2 $$-$$ 2x $$-$$ 2y + 1 = 0 Circle P : x2 + y2 $$-$$ 2y = 0 If the centre of circle M is joined with centre of the circle N, further center of circle N is joined with centre of the circle O, centre of circle O is joined with the centre of circle P and lastly, centre of circle P is joined with centre of circle M, then these lines form the sides of a :

Let S1 : x2 + y2 = 9 and S2 : (x $$-$$ 2)2 + y2 = 1. Then the locus of center of a variable circle S which touches S1 internally and S2 externally always passes through the points :

Let r1 and r2 be the radii of the largest and smallest circles, respectively, which pass through the point ($$-$$4, 1) and having their centres on the circumference of the circle x2 + y2 + 2x + 4y $$-$$ 4 = 0. If {{{r_1}} \over {{r_2}}} = a + b\sqrt 2, then a + b is equal to :

Let the circle S : 36x2 + 36y2 $$-$$ 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x $$-$$ 2y = 4 and 2x $$-$$ y = 5 lies inside the circle S, then :

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $$6\sqrt{5}$$ on the x-axis. Then the radius of the circle C is equal to :

Two tangents are drawn from the point P($$-$$1, 1) to the circle x2 + y2 $$-$$ 2x $$-$$ 6y + 6 = 0. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to :

Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :

Let $$A=\{(x,y)\in R\times R|2x^2+2y^2-2x-2y=1\}$$, $$B=\{(x,y)\in R\times R|4x^2+4y^2-16y+7=0\}$$ and $$C=\{(x,y)\in R\times R|x^2+y^2-4x-2y+5\le r^2\}$$. Then the minimum value of |r| such that $$A\cup B\subseteq C$$ is equal to

If a line along a chord of the circle 4x2 + 4y2 + 120x + 675 = 0, passes through the point ($$-$$30, 0) and is tangent to the parabola y2 = 30x, then the length of this chord is :

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y $$-$$ 5 = 0 at two points P and Q such that PQ is a diameter of C1. Then the diameter of C is :

Let Z be the set of all integers, $$A=\{(x,y)\in Z\times Z:(x-2{)}^2+y^2\le 4\}$$ $$B=\{(x,y)\in Z\times Z:x^2+y^2\le 4\}$$ $$C=\{(x,y)\in Z\times Z:(x-2{)}^2+(y-2{)}^2\le 4\}$$ If the total number of relation from A $$\cap$$ B to A $$\cap$$ C is 2p, then the value of p is :