Question

The radii of two concentric circles are 41cm and 40cm.A chord of the circle with bigger radius touches the circle with smaller radius . Find the length of that chord​

Answer 1

Answer:

let AB is a chord of big circle and tengent to the small circle which bisect at M ,O is the centre of two concentric circles

by using Pythagoras method

${am}^{2} = {oa}^{2} - {om}^{2} \\ {am}^{2} = {41}^{2} - {40 }^{2} \\ = (41 - 40)(41 + 40) \\ = (1)(81) = 81 \\ {am}^{2} = 81 \\ am = \sqrt{81} \\ am = 9 \\ ab = 2am \\ ab = 2 \times 9 \\ ab = 18$

so the length of chord is 18cm