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