Answer:
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Connect the center with the point of tangency.
It will make a right triangle with legs 16 and 12.
Use Pythagorean theorem to set up an equation, then solve it for x.
The hypotenuse of the triangle is:
- -2x + 34 + 12 =
- - 2x + 46
It needs to be a positive length, so:
- -2x + 46 > 0 ⇒ 46 > 2x ⇒ 23 > x ⇒ x < 23
The equation:
- (-2x + 46)² = 16² + 12²
- 4(-x + 23)² = 4(8²) + 4(6²)
- (-x + 23)² = 8² + 6²
- (-x + 23)² = 100
- (-x + 23)² = 10²
- - x + 23 = ± 10
- x = 13 or x = 33
The second root (x = 33) is discarded as greater than 23, so the answer is x = 13.