CIRCLE - 2

Find the value of y.

solution

From circle geometry,

(QR)(QS) = (PQ)²

y(y + 9) = 6²

y² + 9y = 36

y² + 9y – 36 = 0

By factorization

y² + 12y – 3y – 36 = 0

(y² + 12y) – (3y – 36) = 0

y(y + 12) – 3(y + 12) = 0

(y - 3 )( y + 12) = 0                             

y - 3 = 0  OR  y + 12 = 0

y = 3 OR y = -12 

Since we don’t have negative length, we take y=3cm