The circles having radii `r_1a n dr_2` intersect orthogonally. The length of their common chord is `

Give two circles intersecting orthogonally having the length of common chord 24//5 units. The radius of one of the circles is 3 units. The angle between direct common tangents is

The circles x^2+y^2 +2x +4y-20=0 and x^2 +y^2 + 6x-8y + 10 = 0 a) are such that the number of common tangents on them is 2 b) are orthogonal c) are such that the length of their common tangents is 5(12/5)^(1/4) d) are such that the length of their common chord is 5sqrt3/2

Two circles C_1 and C_2 intersect in such a way that their common chord is of maximum length. The center of C_1 is (1, 2) and its radius is 3 units. The radius of C_2 is 5 units. If the slope of the common chord is 3/4, then find the center of C_2dot

Circles of radius 5 units intersects the circle (x-1)^(2)+(x-2)^(2)=9 in a such a way that the length of the common chord is of maximum length. If the slope of common chord is (3)/(4) , then find the centre of the circle.

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Two circles with centres O and O' of radii 3cm and 4 cm, respectively intersect at two points P and Q, such that OP and O' P are tangents to the two circles. Find the length of the common chord PQ.

If theta is the angle between the two radii (one to each circle) drawn from one of the point of intersection of two circles x^2+y^2=a^2 and (x-c)^2+y^2=b^2, then prove that the length of the common chord of the two circles is (2a bsintheta)/(sqrt(a^2+b^2-2a bcostheta))

If the curves y=2e^(x)andy=ae^(-x) intersect orthogonally, then a = __________

Two fixed circles with radii r_1a n dr_2,(r_1> r_2) , respectively, touch each other externally. Then identify the locus of the point of intersection of their direction common tangents.