Question

What is the length of a chord which is 12 cm from the center of a circle with radius 15 cm?

Answer 1

AP= BP = AB/2 = x/2

In AOP,

∠APO = 90°

By Pythagoras,

(AO)^2 = (AP)^2 + (OP)^2

(15)^2 = (x/2)^2 + (12)^2

225 = x^2/4 + 144

x^2/4 = 225 - 144

x^2 /4 = 81

x^2 = 81 ×4

x^2 = 324

x = 18 cm

Answer 2

Answer:

18 m.

Step-by-step explanation:

Let the length of the chord be 2a.

From the figure, using Pythagoras theorem :

   ⇒ ( distance b/t center & chord )^2 + ( a )^2 = radius^2

   ⇒ ( 12 m )^2 + a^2 = ( 15 m )^2

   ⇒ a^2 = 225 m^2 - 144 m^2

   ⇒ a^2 = 81 m^2

   ⇒ a = 9 m

 Thus,

     Length of chord is 2( a ) or 2( 9  m ) or 18 m.