CIRCLES B2

Find x on the following figure

solution

According to rectangle properties of a circle

(CX)(XD) = (AX)(XB)

(x)(x + 3) = (5)(2)

x² + 3x = 10

x² + 3x – 10 = 0 [ solving by factorization ]

x² + 5x – 2x – 10 = 0 [ splitting 3x into 5x and (-2x) ]

x(x + 5) – 2(x + 5) = 0

 (x + 5) (x - 2) = 0

x + 5 = 0 or x - 2 = 0

x = -5 or x = 2

Since there is no negative length, we take x=2cm.