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