To find the appropriate relationships based on the given information, let's use the formulas that relate radius (r), diameter (d), and circumference (C) of a circle:
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The diameter is related to the radius by: \[ d = 2r \]
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The circumference is related to the radius by: \[ C = 2\pi r \]
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The circumference is also related to the diameter by: \[ C = \pi d \]
Now let's analyze the provided options:
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If d = 20 and C = 20π: \[ C = \pi d \quad \implies \quad 20\pi = \pi \cdot 20 \quad \text{(true)} \] Radius \( r \) can be calculated as: \[ r = \frac{d}{2} = \frac{20}{2} = 10 \]
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If d = 26 and C = 26π: \[ C = \pi d \quad \implies \quad 26\pi = \pi \cdot 26 \quad \text{(true)} \] Radius \( r \): \[ r = \frac{d}{2} = \frac{26}{2} = 13 \]
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If r = 6 and C = 12π: \[ C = 2\pi r \quad \implies \quad 12\pi = 2\pi \cdot 6 \quad \text{(true)} \]
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If r = 50 and C = 100π: \[ C = 2\pi r \quad \implies \quad 100\pi = 2\pi \cdot 50 \quad \text{(true)} \]
Now, we can use the relationships derived to match each set of values to their respective formulas:
- From the first example, we confirmed that \( r = 10 \) for \( d = 20 \) and \( C = 20\pi \).
- From the second, \( r = 13 \) for \( d = 26 \).
- From the third, \( C = 12\pi \) is valid for \( r = 6 \).
- From the fourth, \( C = 100\pi \) holds for \( r = 50 \).
In conclusion:
- For If d = 20 and C = 20π, then \( r = 10 \).
- For If d = 26 and C = 26π, then \( r = 13 \).
- For If r = 6 and C = 12π, this is valid.
- For If r = 50 and C = 100π, this is also valid.
Therefore, the relationships have been confirmed and successfully matched.