\]Question: An environmental educator in Toronto is planning a circular garden with a diameter of 10 meters for a school project. A straight walking path of 6 meters is to be laid across the garden, not passing through the center. What is the shortest distance from the center of the garden to this path?

["Title: How to Find the Shortest Distance from the Garden Center to a Crosswalk in a Circular Garden", "When designing a circular garden—as exemplified by a Toronto school project featuring a 10-meter diameter plot—adding a functional element like a walking path requires careful planning. This article explains how to calculate the shortest distance from the garden center to a straight 6-meter path that runs across the circle but avoids the center.", "### Understanding the Problem", "You have a circular garden with a diameter of 10 meters, so its radius is 5 meters. A straight walking path of 6 meters crosses the garden, but it does not pass through the center. The goal is to determine the shortest distance from the center of the garden to this non-central path.", "### Key Concept: Perpendicular Distance from Center to Chord", "In a circle, the shortest distance from the center to any chord (such as the walking path) is the perpendicular distance. This forms a right triangle:", "- The hypotenuse is the radius (5 meters),\n- One leg is half the length of the chord (path),\n- The other leg is the shortest distance from the center to the path.", "Given:\n- Chord length = 6 meters → half-length = 3 meters\n- Radius = 5 meters", "Using the Pythagorean theorem:\n[\n\ ext{Distance}^2 + 3^2 = 5^2\n]\n[\n\ ext{Distance}^2 = 25 - 9 = 16\n]\n[\n\ ext{Distance} = \sqrt{16} = 4 \ ext{ meters}\n]", "### Final Answer", "The shortest distance from the center of the garden to the 6-meter walking path is 4 meters.", "### Why This Matters in Garden Design", "Precise calculations like this ensure the path fits well within the educational garden while preserving space for planted beds around the circular perimeter. Knowing exact distances helps educators and students visualize spatial relationships and make informed design decisions.", "### Summary", "- Circle radius = 5 m\n- Path length = 6 m → half = 3 m\n- Shortest distance from center to path = 4 m", "This geometric insight supports effective and sustainable outdoor learning environments."]