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.
