property of secants

Question

Find value of x

Answer 1

The chords  from the intersection of the chords rule MO(MO+OP)=MN(MN+NE)

MO=x, OP=3, MN=5, NE=9

substitute the values in MO(MO+OP)=MN(MN+NE)

x(x+3)=5(5+9)

x²+3x=5×14

x²+3x=70

Subtract 70 from each sides

x²+3x-70=70-70

x²+3x-70=0

x²+10x-7x-70=0                   (Factors on the left side)

x(x+10)-7(x+10)=0

(x+10) (x-7)=0                       (Zero product property)

x+10=0   or  x-7=0  

x=-10    or x=7

The value of x is -10, 7.