perplexus.info :: Geometry : Find the arc

Find the arc (Posted on 2018-02-08)

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 3 |

(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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