Question

Picture included What is the value of X for the picture

Answer 1

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

$\Rightarrow 8(x+13)=9(x+10)$

$\Rightarrow 8x+104=9x+90$

Subtract 90 from both sides.

$\Rightarrow 8x+104-90=9x+90-90$

$\Rightarrow 8x+14=9x$

Subtract 8x from both sides.

$\Rightarrow 8x+14-8x=9x-8x$

$\Rightarrow 14=x$

The value of x is 14.