Question

Someone help me. I've been trying to do this one my own. But I just can't.

Answer 1

9514 1404 393

Answer:

  1) x = 4

  2) ? = 20

  8) x = 5

Step-by-step explanation:

Use the applicable relationships to write an equation involving the unknown. Solve the equation.

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1) We note that the marked arcs are the same length. In a circle, chords that subtend arcs of the same measure are the same length.

  5x -1 = 4x +3

  x = 4 . . . . . . . . . . add 1-4x to both sides

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2) A tangent meets a radius at right angles. The given triangle is a right triangle, so the Pythagorean theorem applies.

  12² +16² = x²

  144 +256 = x² = 400

  x = √400 = 20

The missing value is 20.

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8. Tangents from the same point are the same length.

  4x -8 = 12

  4x = 20 . . . . . add 8

  x = 5 . . . . . . . divide by 4

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Additional comment

In problem 2, you note the ratio of side lengths is 12 : 16 = 3 : 4. This should give you a clue that this is a 3-4-5 right triangle. The long (missing) side will be 5, scaled by the scale factor of 4, so will be 4×5 = 20.