CIRCLES 1

Find y in the figure below

From circle geometry,

(QR)(QS) = (PQ)²

y(y + 16) = 6²

y² + 16y = 36

y² + 16y – 36 = 0

We factorize by splitting the middle term. 16y = (– 2y + 18y).

y² + 18y – 2y – 36 = 0

(y² + 18y) – (2y – 36) = 0

y(y + 18) – 2(y + 18) = 0

(y - 2)( y + 18) = 0                              

y - 2 = 0  OR  y + 18 = 0

y = 3 OR y = -18 

Since we don’t have negative length, we take y=2cm

TRY THIS……..

Find y in the figure below;