SOLUTION: 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 t

Algebra ->  Algebra  -> Circles -> SOLUTION: 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 t      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 327055: 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
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
If we draw a picture, we can see that the radius of the wheel has length
R=10+x or R=5+y............[1]
The equation of a circle is x%5E2%2By%5E2=R%5E2
From [1], we see that x=R-10 and y=R-5
This gives us
%28R-10%29%5E2%2B%28R-5%29%5E2=R%5E2
Now, we have to down to one variable.
Simplify and form a quadratic:
R%5E2-30R%2B125=0
R=5
R=25
Of course, 5 is extraneous and we find the wheel has radius 25 inches.