Question

I need help! Someone pls help meh :)

Answer 1

Here you have two secants, so you need to know this:

Answer 2

so i would add them?

Answer 3

i don't get it

Answer 4

For each secant,
1. Add the segment of the secant outside the circle to the secant.
2. Multiply the segment outside the secant by the entire secant.
3. Set the products equal and solve for x.

Answer 5

would it be 7?

Answer 6

\(x (x + 3x) = 8(8 + x + 4) \)

Answer 7

\(x (x + 3x) = 8(8 + x + 4) \)

\(x(4x) = 8(x + 12)\)

\(4x^2 = 8x + 96\)

\(4x^2 - 8x - 96 = 0\)

\(x^2 - 2x - 24 = 0\)

\((x+ 4)(x - 6) = 0\)

\(x + 4 = 0\) or \(x - 6 = 0\)

\(x = -4\) or \(x = 6\)

If you use x = -4, then the length of ZU is -4.
A length cannot be negative, so you discard x = -4.

You keep the solution x = 6.
Now plug in x = 6 in x + 4 to find the length of TW.