Thread: Geometry Word Problem (Arcs)

A bridge over a river has a shape of a circular arc. The span of the bridge is 24 meters. (The span is the length of the chord of the arc.) The midpoint of the arc is 4 meters higher than the endpoints. What is the radius of the circle that contains this arc?

The radius = 20, I'm not sure how to get to that answer, though.


Thanks in advance.

Hello, dvh9!

A bridge over a river has a shape of a circular arc.
The span of the bridge is 24 meters. (The span is the length of the chord of the arc.)
The midpoint of the arc is 4 meters higher than the endpoints.
What is the radius of the circle that contains this arc?

Code:

                C
              * * *
          *    4|     *
      A *-------o-------* B
       *  * 12  |D    *  *
            *   |   * R
      *       * | *       *
      * - - - - * - - - - *
                O

The center of the circle is
The radius is: .
, hence: .



In right triangle

So we have: .

. .

Therefore, the radius of the arc is 20 meters.

Wonderful description, thanks!