Question

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

Answer 1

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

so 18 cm is your answer