A drone flies over a circular crop field with a radius of 200 meters. It flies along a chord that is 300 meters long. How far is the chord from the center of the circle, in meters?

["How Far Is a 300-Meter Chord From the Center of a Circular Crop Field With a 200-Meter Radius?", "In agricultural technology and precision farming, drones play a vital role—automatically mapping and monitoring crop fields. Recently, an intriguing scenario unfolded: a drone flying precisely over a circular crop field with a 200-meter radius, tracing a chord 300 meters long. But a key question arises: how far is this chord located from the center of the circle? Understanding this distance helps in interpreting drone imagery and planning optimal flight paths.", "## The Geometry Behind the Chord", "A circular field with radius 200 meters contains a chord measuring 300 meters. To determine the perpendicular distance from the center of the circle to this chord, we apply a fundamental geometric principle: the perpendicular from the center of a circle to a chord bisects the chord and forms two right triangles.", "### Step-by-Step Calculation", "1. Identify known values:\n - Radius ( r = 200 ) meters\n - Chord length = 300 meters → Half of the chord = ( \frac{300}{2} = 150 ) meters", "2. Visualize the right triangle:\n The perpendicular distance from the center to the chord (let’s call it ( d )) creates a right triangle with:\n - Hypotenuse = radius = 200 m\n - One leg = half the chord = 150 m\n - Other leg = perpendicular distance ( d ) (unknown)", "3. Apply the Pythagorean theorem:\n [\n r^2 = d^2 + \left(\frac{\ ext{chord length}}{2}\right)^2\n ]\n [\n 200^2 = d^2 + 150^2\n ]\n [\n 40,000 = d^2 + 22,500\n ]\n [\n d^2 = 40,000 - 22,500 = 17,500\n ]\n [\n d = \sqrt{17,500}\n ]\n Simplify:\n [\n \sqrt{17,500} = \sqrt{25 \ imes 700} = 5\sqrt{700} = 5\sqrt{100 \ imes 7} = 5 \ imes 10 \ imes \sqrt{7} = 50\sqrt{7}\n ]\n Numerically, ( \sqrt{7} \approx 2.64575 ), so:\n [\n d \approx 50 \ imes 2.64575 \approx 132.29 \ ext{ meters}\n ]", "## Conclusion: Distance From Center to the Drone’s Flight Path", "The drone flies along a chord of length 300 meters across a circular crop field with a 200-meter radius. The shortest distance from the center of the field to this flight path is approximately 132.29 meters.", "This insight confirms how drones strategically navigate beyond the central axis to capture full-field imagery—critical for accurate crop monitoring and data collection. Knowledge of such geometric relationships enhances agricultural drone operations, ensuring optimal coverage and data quality.", "---", "Keywords: drone flight path, circular crop field, chord distance center, geometry of circles, precision agriculture, agricultural drone, chord length calculation, circular geometry, radius and chord distance, agricultural mapping.", "---", "By understanding that the chord lies about 132.29 meters from the center, farmers, agronomists, and drone operators can better plan flight patterns and position sensors for maximum field coverage."]