Question

A chord AB of a circle is at a distance of 6cm from the centre of a circle whose radius is 6cm less than the chord AB. Find the length of the chord and radius of the circle

Answer 1

let the length of the cord be x cm and the perpendicular from the centre to the cord be OP 
so AP =x/2 (since perpendicular from centre to cord bisects the cord )
in rt triangle OPA

OA​2= AP2+ OP2

i.e.  (x-6)2= (x/2)2+ 62
      x2-12x +36  = x2/4 +36

implies  x2-12x =x2 /4
            4x2-48x = x2
           3x2-48x  = 0
               x2  -16x  = 0
                 x2 = 16x
​               x2/x =16
                  x= 16cm

therefore the length of the cord is 16cm and the radius is 10 cm

Answer 2

Answer:

Hope it helps

Step-by-step explanation: