SOLUTION: a circular park 80 meters in diameter has a straight path cutting across it. it is 24 meters from the center of the park to the closet point on this path. how long is the path?

Question 148693: a circular park 80 meters in diameter has a straight path cutting across it. it is 24 meters from the center of the park to the closet point on this path. how long is the path?
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
This is a good problem. Analyzing it, that 24 meters from the center of the park to the closest point of this straight path cutting is only possible if it is perpendicular. Draw it on a diagram and you'll see why.
Now that forms two oppposite right triangle, with equal measurements and hypotenuse of each is the radius = 40 meters---- mark "c". Also mark "a" the 24 meters, from the center perpendicular to the middle of the path cutting.
.
Focusing on 1 triangle, we'll get half of the total length of the path cutting then right?---- mark this as ----->unknown oks?
Therefore by Pythagorean Theorem,

Since that's only 1 triangle showing half of the length, we multiply it by 2 to get the full length of the path cutting, ---> final answer.
Thank you
Jojo

RELATED QUESTIONS
A circular park 80 meters in diameter has a straight path cutting across it. It is 24... (answered by josmiceli)
A rectangular park is 93 meters long and 86 meters wide. It has a path 1.5 meters around... (answered by josgarithmetic)
a park has a 5-foot wide straight path from one end of the park to the other. If the area (answered by stanbon)
A park has just installed a circular fountain in 8 meters diameter. The park wants to... (answered by Theo)
a rectangular park is 20 miles long and 10 meters wide, How long is the route diagonally... (answered by solver91311)
two sides of a rectangular park are 50 meters and 120 meters long. A path runs diagonally (answered by ewatrrr)
A circular path has a diameter of 120 meters. a person average walking speed is 4... (answered by ankor@dixie-net.com)
A circular path has a diameter of 120 meters. your average walking speed is 4 kilometers... (answered by Alan3354)
a circular flower bed is 6 m in diameter and has a circular sidewalk around it 1 meter... (answered by JBarnum)