SOLUTION: Wagon wheel. A wagon wheel is placed against a wall as shown in the accompanying figure. One point on the edge of the wheel is 5 inches from the ground and 10 inches from the wa

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Question 204051This question is from textbook
: Wagon wheel. A wagon wheel is placed against a wall as
shown in the accompanying figure. One point on the edge
of the wheel is 5 inches from the ground and 10 inches
from the wall. What is the radius of the wheel?
Thank you for all your help i really appreciate it. This question is from textbook

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming it's tangent to the wall and the ground:
Let the ground be the x-axis and the wall the y-axis
The eqn of the circle is:
(x-r)^2 + (y-r)^2 = r^2
Sub 10 for x and 5 for y, since the point (10,5) is on the circle.
100-20r+r^2 + 25-10r+r^2 = r^2
r^2 -30r + 125 = 0
r = 5 (the point is at the top of the wheel. This point is inverted, 10 from the ground and 5 from the wall.)
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r = 25 (the point is below the axle of the wheel)