Answer:
Step-by-step explanation:
What this formula says is that the external segment of the secant * the secant's entire length = the tangent squared
16
(x+2)^2 = 18(18 + 14) Add what is inside the brackets
(x +2)^2 = 18 * 32 Combine the right
(x + 2)^2 = 576 Take the square root of both sides
√(x + 2)^2 = √576
x + 2 = 24 Subtract 2 from both sides
x = 24 - 2
x = 22
I don't think you can use the minus value here.
14
Two secant theorem
The two secant theorem has both the left and right set up as having brackets.
8(19 + 8) = (x + 4)(3x + x+4) Simplify the right and left
8(27) = (x + 4)(4x + 4) Remove the right and left brackets
216 = 4(x + 4)( x + 1) Expand the right
216 = 4 (x^2 + 5x + 4) Divide both sides by 4
54 = x^2 + 5x + 4 Subtract 54 from both sides
x^2 + 5x - 50 Combine the left
x^2 + 5x - 50 = 0 Factor
(x + 10)(x - 5) = 0
I think the only usable factor is x - 5 = 0
x = 5
