A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is

Question

Philoid · Accepted Answer

Let AB and CD be two chords of the circle.

Draw OM perpendicular to AB and ON = CD

AB = 14 cm

OM = 6 cm

ON = 2 cm

Let,

CD = x

In AOM,

AO² = AM² + OM²

= 7² + 6²

AO² = 85 (i)

In CON,

CO² = ON² + CN²

CO² = 4 + (ii)

We Know,

AO = CO

AO² = CO²

85 = 4 +

x² = 324

x = 18 cm