Question

Find the value of x - this is circle segments.

Answer 1

Given:

Diagram of a circle and its two secant from an exterior point.

To find:

The value of x.

Solution:

We know that, If two secant are on a circle from an exterior point, then the products of measure of secants and measure of external segments of secants are equal.

Using the above property, we get

`(x+7)x=(2+2)2`

`x^2+7x=(4)2`

`x^2+7x=8`

`x^2+7x-8=0`

Splitting the middle term, we get

`x^2+8x-x-8=0`

`x(x+8)-1(x+8)=0`

`(x+8)(x-1)=0`

Using zero product property, we get

`(x+8)=0` and
`(x-1)=0`

`x=-8` and
`x=1`

Side cannot be negative.

Therefore, the only possible value of x is 1.