QQuestionMathematics
QuestionMathematics
How do you find the scale factor of two similar circles?
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand Similar Circles
Similar circles are circles that have the same shape but different sizes. The scale factor describes the relationship between their radii or diameters.
Step 3:: Define Scale Factor
The scale factor (k) is the ratio of corresponding linear dimensions between two similar circles. This can be calculated by dividing the radius (or diameter) of one circle by the radius (or diameter) of the other circle.
Step 4:: Scale Factor Formula
- $$r_{2}$$ is the radius of the second circle
The scale factor can be expressed as: Where:
Step 5:: Alternative Calculation Methods
- Circumferences: $$k = \frac{C_{1}}{C_{2}}
You can also calculate the scale factor using:
Step 6:: Important Considerations
- If $$k = 1$$, the circles are identical
- The scale factor is always a positive real number
Final Answer
To find the scale factor of two similar circles, divide the linear dimension (radius, diameter, or circumference) of one circle by the corresponding linear dimension of the other circle: k = \frac{r_{1}}{r_{2}}.
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