Question

two concentric circles of radii a and b (a>b) are given. Find the length of the chord of the larger circle which touches the smaller circle

Answer 1

chord of larger circle will be the tangent to smaller. using this property we get that b is perpendicular to chord cd and bisects it. using pythagoras theorem the length if chord is 2times root of a^2 -b^2

Answer 2

angle OEC=90(tangent and radius at point of contact are perpendicular)

by Pythagoras theorem
OC^2=OE^2+CE^2
a^2=b^2+CE^2
√(a^2-b^2)=CE
CD=2CE[perpendicular drawn from centre bisect the chord]
CD=2√(a^2-b^2)