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What is the value of x?

What Is The Value Of X class=

Sagot :

Answer:

B

Step-by-step explanation:

Since UV is a tangent then ∠ WUV = 90°

WZ = WU = x - 1 ( both radii of the circle ) , then

WV = x - 1 + 2 = x + 1

Using Pythagoras' identity in the right triangle

WU² + UV² = WV² , that is

(x - 1)² + (2x - 4)² = (x + 1)² ← expand factors using FOIL

x² - 2x + 1 + 4x² - 16x + 16 = x² + 2x + 1

5x² - 18x + 17 = x² + 2x + 1 ← subtract x² + 2x + 1 from both sides

4x² - 20x + 16 = 0 ← divide through by 4

x² - 5x + 4 = 0

(x - 1)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

But x ≠ 1 as radius x - 1 = 0

Thus x = 4 → B

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