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The lines that appear tangent are tangent. What is the value of x, to the nearest tenth.

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x ≈ 10.7

Step-by-step explanation:

Is given in the picture that x is the radius of the circle.

The radius of a circle and the tangent line to the circle form a right angle, therefore our triangle is a right triangle.

We can apply the Pythagorean Theorem to find one equation that will have one unknown x.

(x+12)² = x² +20² , use that (a+b)² = a²+b²+2ab

x²+12²+2·x·12 = x² +20², subtract x² from both sides of the equation

12² + 24x = 20², subtract 12² from both sides of the equation

24x = 20²-12², raise to power and combine like terms

24x = 256, divide by 24 both sides of the equation

x = 10.6666666..., round to the nearest tenth

x ≈ 10.7
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