SOLUTION: If I have a circle with a radius of 40" and a horizontal tangent line, if I move 2.25" along the tangent line from the point where it contacts the circle, what is the distance to t

Algebra ->  Circles -> SOLUTION: If I have a circle with a radius of 40" and a horizontal tangent line, if I move 2.25" along the tangent line from the point where it contacts the circle, what is the distance to t      Log On


   

Question 761404: If I have a circle with a radius of 40" and a horizontal tangent line, if I move 2.25" along the tangent line from the point where it contacts the circle, what is the distance to the circle.
Thanks in advance.
Steve
sgray125@yahoo.com
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
hi Steve,
Draw your circle.
Draw a horizontal line along the bottom
of your circle just touching at one point.(Call it P)
Draw a radius from the centre ( C )of your circle
down to P.
Now if you move 2.25" along from point P
to say point R.
Now join up point R with the centre of the circle (C) and
you have a right angled triangle CPR
Right angled at P.
Now, CP^2 + PR^2 = CR^2 (Pythagoras)
40^2 = 2.25^2 = CR^2
CR^2 = 1605.06
CR = sqrt%281605.06%29
CR = 40.06" (2 decimal places)
Now as CR is made up of the radius and the piece
between Point R and the circle. If we remove the
size of the radius from the size of CR we will
be left with the distance from Point R to the
circle.
40.06 - 40 = 0.06"
Hope this helps Steve.
:-)