Two parallel chords of a circle of radius 2 are at a distance. `sqrt3+1` apart. If the chord subtend angles `pi/k` and `(2pi)/k` at the center, where `k >0,` then the value of [k] is

Two parallel chords of a circle of radius 2 units are (sqrt3+1) units apart. If these chords subtend, at the centre, angles of 90^@ /k" and "180^@/k , where kgt0 , then find the value of k.

Two chords of a circle are of lengths a cm and b cm and they subtend angles theta and 3theta respectively at the center of the circl. If the radius of the circle by r cm, show that, r=a sqrt(a/(3a-b)) cm.

If the chord u=mx +1 of the circel x ^(2) +y^(2)=1 subtends an angle of 45^(@) at the major segment of the circle, then the value of m is-

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))

If the chord y = mx + 1 subtends an angle of measure 45^0 at the major segment of the circle x^2+y^2=1 then value of 'm' is

Area of the circle in which a chord of length sqrt2 makes an angle pi/2 at the centre is

If the chord of contact of the tangents drawn from the point (h , k) to the circle x^2+y^2=a^2 subtends a right angle at the center, then prove that h^2+k^2=2a^2dot

If k, 2(k+1), 3(k+1) are in GP, Then find the value of k.

If two chords AB and AC of a circle with center at O lie in the opposite side of the radius OA, then angle OAB = angle OAC