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First, look closely: The image displays a geometry problem involving a circle. A diameter is shown with a length of 22.4. A chord, labeled 8.8, is perpendicular to the diameter. The distance from the center of the circle to this chord is labeled 'x', which is the unknown we need to find. The problem is presented as a multiple-choice question with options A) 5, B) 4.3, C) 4.4, D) 3.1.
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Next, find information: This is a standard geometry problem that can be solved using the Pythagorean theorem. I will calculate the value of 'x' based on the given lengths.
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Then, review the findings: The radius of the circle is half the diameter, so it is 22.4 / 2 = 11.2. The perpendicular from the center to the chord bisects the chord, so half the chord length is 8.8 / 2 = 4.4. We now have a right triangle where the hypotenuse is the radius (11.2), one leg is half the chord (4.4), and the other leg is 'x'. Using the Pythagorean theorem: x² + 4.4² = 11.2². Solving for x gives us x = √(11.2² - 4.4²) = √(125.44 - 19.36) = √106.08 ≈ 10.3. This result does not match any of the provided options, indicating a potential error in my initial interpretation or calculation. I will re-examine the diagram to ensure I correctly identified the elements.
Parent Tip: Review the logic above to help your child master the concept of arcs and chords worksheet.
