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DochEvi [55]
3 years ago
5

What is the length of the tangent line in the picture?

Mathematics
1 answer:
S_A_V [24]3 years ago
4 0

Answer:

x = -2

Step-by-step explanation:

The tangent line has length "x + 8"

The secant line has length "x + 6 + 5", where

5 is the inner part

x + 6 is the outer part

Now,

the secant-tangent theorem tells us that square of the tangent line is equal to the outer segment of secant line multiplied by length of whole secant line.

So, we can say:

(x+8)^2 = (x+6)(x+6+5)

We can solve for x shown below:

(x+8)^2 = (x+6)(x+6+5)\\(x+8)^2=(x+6)(x+11)\\x^2+16x+64=x^2+17x+66\\17x-16x=64-66\\x=-2

The value of x is -2

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