Two equal circles of radius `r` intersect such that each passes through the centre of the other. The length of the common chord of the circles is `sqrt(r)` (b) `sqrt(2)\ r\ A B` (c) `sqrt(3)\ r\ ` (d) `(sqrt(3))/2\ r`

The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length, is (a) sqrt(5)\ c m (b) 2sqrt(5)\ c m (c) 2\ sqrt(7)\ c m (d) sqrt(7)\ c m

The length of the common chord of two circles of radii r_1 and r_2 which intersect at right angles is

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is (2+sqrt(3))r (b) ((2+sqrt(3)))/(sqrt(3))r ((2-sqrt(3)))/(sqrt(3))r (d) (2-sqrt(3))r

The circles having radii r_1 and r_2 intersect orthogonally. Find the length of their common chord.

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

In a circle with centre O ,\ A B\ a n d\ C D are two diameters perpendicular to each other. The length of chord A C is (a) 2A B (b) sqrt(2)AB (c) 1/2A B (d) 1/(sqrt(2))\ A B

The circles having radii r_1a n dr_2 intersect orthogonally. The length of their common chord is (2r_1r_2)/(sqrt(r1^2+r2^2)) (b) (sqrt(r1^2+r2^2))/(2r_1r_2) (r_1r_2)/(sqrt(r1^2+r1^2)) (d) (sqrt(r1^2+r1^2))/(r_1r_2)

Two tangents making an angle of 120^0 with each other are drawn to a circle of radius 6cm, then the length of each tangent is equal to sqrt(3) cm (b) 6 sqrt(3) cm (c) sqrt(2) cm (d) 2 sqrt(3) cm

The locus of the mid-points of the chords of the circle of lines radiùs r which subtend an angle pi/4 at any point on the circumference of the circle is a concentric circle with radius equal to (a) (r)/(2) (b) (2r)/(3) (c) (r )/(sqrt(2)) (d) (r )/(sqrt(3))