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
[tex](x+7)x=(2+2)2[/tex]
[tex]x^2+7x=(4)2[/tex]
[tex]x^2+7x=8[/tex]
[tex]x^2+7x-8=0[/tex]
Splitting the middle term, we get
[tex]x^2+8x-x-8=0[/tex]
[tex]x(x+8)-1(x+8)=0[/tex]
[tex](x+8)(x-1)=0[/tex]
Using zero product property, we get
[tex](x+8)=0[/tex] and [tex](x-1)=0[/tex]
[tex]x=-8[/tex] and [tex]x=1[/tex]
Side cannot be negative.
Therefore, the only possible value of x is 1.
