two circles of radii 10 cm and 17 cm intersect at two points and distance between their centers is 21 cm.find length of common chord

Answer 1

Make a sketch.
draw a radius from the each of the circles to the points of contact of the common tangent.
Those two radii will be parallel
joint the two centres.
draw a perpendicular from the centre of the smaller circle to the larger radius.

You will see a right-angled triangle with hypotenuse 21, one short side of 7 and the other leg will be the length of the common tangent.

x^2 + 7^2 = 21^2
x^2 = 392
x = √392 = .....