CIRCLES 3

Find y in the figure below;

Solution

From circle geometry,

(QR)(QS) = (PQ)²

y(y + 21) = 10²

y² + 21y = 100

y² + 21y – 100 = 0

We factorize by splitting the middle term: 21y = (25y – 4y).

y² + 25y – 4y – 100 = 0

(y² + 25y) – (4y – 100) = 0

y(y + 25) – 4(y + 25) = 0

(y - 4)( y + 25) = 0                              

y - 4 = 0  OR  y + 25 = 0

y = 4 OR y = -25 

Since we don’t have negative length, we take y = 4cm

TRY THIS……..

Find y in the figure below;