Answer:
x = 9
Step-by-step explanation:
The angle formed by the tangent BC and the radius AB is right at B
Thus ΔABC is right with AC as the hypotenuse
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, hence
AC² = AB² + BC² ← substitute given values
(x + 6)² = x² + 12² ← expand squared parenthesis on left side
x² + 12x + 36 = x² + 144 ( subtract x² from both sides )
12x + 36 = 144 ( subtract 36 from both sides )
12x = 108 ( divide both sides by 12 )
x = 9
