Question

What is the power of x? A) 2 B) 3 C) 6 D) 7

Answer 1

Answer:

A

Step-by-step explanation:

They are basically wanting the value of x.

These are 2 secant lines drawn. Secant Line is a line that intersects the circle at 2 points.

To solve this, we have to use secant-secant theorem.

Secant-Secant Power Theorem tells us that if 2 secant lines are drawn from external point (here, E) to a circle, then, product of measure of one secant's external part and total secant is equal to other secants external part and whole secant.

In algebra, that is:

$(x+1)(x+1+11)=(x+4)(x+4+1)$

Let's multiply and find the value of x:

$(x+1)(x+1+11)=(x+4)(x+4+1)\\(x+1)(x+12)=(x+4)(x+5)\\x^2 + 13x + 12=x^2+9x+20\\13x+12=9x+20\\13x - 9x = 20 - 12\\4x = 8\\x = 2$

Hence, the correct answer choice is A