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Epic Games Installer Ended Prematurely - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: A cartographer uses satellite data to map a circular forest reserve. A straight river crosses the reserve forming a chord of length 14 km, and the shortest distance from the forestâs center to the river is 5 km. What is the area of the forest in square kilometers?

📌 Solution: Let $ r $ be the radius of the forest. The chord length is 14 km, so half is 7 km. The perpendicular distance from the center to the chord is 5 km. Using the Pythagorean Theorem:

📌 r^2 = 5^2 + 7^2 = 25 + 49 = 74

📌 Thus, the area of the forest is:

📌 \pi r^2 = 74\pi

📌 The area is $ oxed{74\pi} $ square kilometers.

📌 Question: An astronomer studies a pulsar whose signal reaches two telescopes on Earth, separated by 1000 km, forming a chord of the apparent circular beam of emission (radius $ 500\sqrt{2} $ km). What is the central angle, in degrees, between the two telescopes as seen from the pulsarâs source?

📌 Solution: The chord length $ c = 1000 $ km, radius $ r = 500\sqrt{2} $

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