Question

What's the value of x? x=

Answer 1

Answer:

x = 2

Step-by-step explanation:

These are 2 secant lines intersecting a circle. This problem can be solved using secant-theorem.

Simply put, the secant theorem tells us that the outer segment (outside the circle) times the total length of secant line (outer and inner segment) is equal to that of the other secant line's product of outer and total.

For this diagram, according to the theorem, it should be:

DE * CE = AE * BE

Hence we have:

$DE * CE = AE * BE\\(1+x+4)*(x+4)=(11+x+1)*(x+1)\\(x+5)*(x+4)=(x+12)*(x+1)\\x^2+9x+20=x^2+13x+12\\20-12=13x-9x\\8=4x\\x=\frac{8}{4}=2$

The value of x is 2