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Find the arc (Posted on 2018-02-08) Difficulty: 3 of 5

Consider a semi-circle of radius r.
A curve C is drawn such that at any point P on C, the distance between P and the semi circle's base equals the length of a line segment from P perpendicular to the given semi-circumference.

Derive C's equation.

No Solution Yet Submitted by Kenny M    
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re: my solution (with spoiler) Comment 2 of 2 |
(In reply to my solution (no spoiler) by armando)

               
      d*     *
  *     i         *
*      b  k        *
 
r= segment dk  
y= segment bi
x= segment bk

r=ik + id 
ik=(x^2+y^2)^1/2
di=bi=y

So: r=(x^2+y^2)^1/2 + y
Then: x^2+y^2 = r^2 + y^2 -2ry => 2ry =r^2 - x^2 =>

y=(r^2-x^2)/2r



  Posted by armando on 2018-02-09 04:05:24
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