Given:
One secant is x+ 5 and 8
Other secant is x + 1 and 9
To find:
The value of x
Solution:
If two secant segments intersect outside a circle, then the product of one segment and its external segment is equal to the product of other segment and its external segment.
External segment = 8 + x + 5 = x + 13
Another external segment = 9 + x + 1 = x + 10
[tex]\Rightarrow 8(x+13)=9(x+10)[/tex]
[tex]\Rightarrow 8x+104=9x+90[/tex]
Subtract 90 from both sides.
[tex]\Rightarrow 8x+104-90=9x+90-90[/tex]
[tex]\Rightarrow 8x+14=9x[/tex]
Subtract 8x from both sides.
[tex]\Rightarrow 8x+14-8x=9x-8x[/tex]
[tex]\Rightarrow 14=x[/tex]
The value of x is 14.
