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.