SOLUTION: I was working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You! I would deeply appreicate it! Circles:Circl

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Question 293123: I was working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You! I would deeply appreicate it!
Circles:Circles and Lengths of Segments
A bridge over a river has the 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?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A bridge over a river has the 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?
:
Solve a right triangle formed by the radius (r), half the chord, and dist from center to the chord
:
r = the hypotenuse
(r-4) = one leg, (dist from center to chord)
12 = one leg (half the length of the chord)
:
r^2 = 12^2 + (r-4)^2
r^2 = 144 + r^2 - 8r + 16
Subtract r^2 from both sides
0 = -8r + 160
8r = 160
r =
r = 20 m is the radius of the circle containing this arc
:
:
Check by solving the right triangle:
distance from center to chord: 20 - 4 = 16
r =
r = 20