Question 759509: MATH QUESTION~
A wheel rests against a floor and a vertical wall. A point P on the rim of the wheel is 2cm and 9cm from the floor and wall respectively Calculate the radius of the wheel.
Please help!
Thank you!
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! If the wheel is resting on the floor and against the wall, the tangent lines are x=0 and y=0 and the points of tangency are (r,0) and (0,r).
The equations for the lines perpendicular to these tangent lines at these points are x=r and y=r and they must go through the center of the circle.
So the center of the circle is (r,r)
The standard form for a circle is (x-a)^2 + (y-b)^2 = r^2 where (a,b) is the center and r is the radius
Since the point P is 2 cm from the floor and 9 cm from the wall, the point is (9,2)
Inserting the point (9,2) in the equation for the circle gives
(9-r)^2 (2-r)^2 = r^2
Simplify and solve for r:
81 - 18r + r^2 + 4 - 4r + r^2 = r^2
r^2 - 22r + 85 = 0
This can be factored as
(r-17)(r-5) = 0
This gives two possible solutions, r=5 cm and r=17 cm
The graph below shows the two circles which share the point (9,2)
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