Ef= 50 - 14x + x^2 eg= 14 - 2x given that ef and eg are tangent lines, apply the tangent segments theorem to set up an equation and solve for x.

x = 3.28

Step-by-step explanation:

Tangent-Segment Theorem : Tangent segments drawn to the same circle from the same point are equal.

Now, EF = 50 - 14·x - x²

and EG = 14 - 2·x

Since, EF and EG are two tangent segments drawn to the same circle, So they both will be equal in length

⇒ 50 - 14·x - x² = 14 - 2·x

⇒ x² + 12·x - 50 = 0

On solving the above equation :

We get, x = 3.28 and x = -15.28

Since, Length of tangent cannot be negative, So we take x = 3.28

Hence, x = 3.28

6

Step-by-step explanation: