Question

What is the value of X?

Answer 1

The problem can be solved using the Power of a Point, which states that:

$EC \cdot ED=EB \cdot EA$.

Substituting

$EC=x+4; ED=x+5; EB=x+1; EA=x+12,$ 

we have the equation

$(x+4) \cdot (x+5)=(x+1) \cdot (x+12)$.

Expanding both sides we get, 

$x^2+9x+20=x^2+13x+12.$

Subtracting $x^2$ from both sides, we have
                           
$9x+20=13x+12$. 
 
Collecting x's and the numbers on two different sides, we have:

4x=8, which finally yields x=2.



Answer: x=2