# Thread: Finding Chords secants and tangents...

1. ## Finding Chords secants and tangents...

Hey could someone help me solve this one:

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

Thanks

2. There are various ways, but you could try.

$(r-4)^{2}+12^{2}=r^{2}$ and solve for r.

3. ## so..

so wanted to make sure I simplified right...r squared plus 16 plus 144 equals r squared?

4. Hello, zachcumer!

so wanted to make sure I simplified right...
r squared plus 16 plus 144 equals r squared? . . . . no
Don't do that!

$(r-4)^2 \;=\;(r-4)(r-4) \;=\;r^2 - 4r - 4r + 16 \;=\;r^2 - 8r + 16$

5. The final part is

r^2-8r+16+144= r^2

So "R" equals 20!

right?

6. Yes, r = 20. Good!.