2023 · Q62
The arch of a bridge is in the form of an arc of a circle. If the span of the bridge is 40 m and height in the middle is 8 m, then what is the radius of curvature of the bridge?
Elementary MathematicsCircles
- A25 m
- B27 m
- C29 m
- D31 m
Explanation
Let the radius of curvature be R. The chord's midpoint gives a right triangle with hypotenuse R, one leg the half-span 20 m, and the other leg R − 8 m. Hence R² = (R − 8)² + 20². Expanding: R² = R² − 16R + 64 + 400, so 16R = 464 and R = 29 m. This matches option (C).