Finding intersection of two curves/ Chord that cuts a circle in ratio 1:3
- To: mathgroup at smc.vnet.net
- Subject: [mg41055] Finding intersection of two curves/ Chord that cuts a circle in ratio 1:3
- From: Sujai <sujai at uiuc.eedduu>
- Date: Wed, 30 Apr 2003 04:23:52 -0400 (EDT)
- Organization: University of Illinois at Urbana-Champaign
- Sender: owner-wri-mathgroup at wolfram.com
I feel like I should know this, but am stuck:
Am trying to find the point along the radius in a circle where, if I
draw a chord perpendicular to the radius, I get a segment that is 1/4th
of the total area of the circle.
For a unit circle (am only working in one quadrant for simplicity), this
would be the point S along the radius, where:
Integrate [Sqrt(1 - x^2), {x, 0, S}] == Pi/8
I used the following code to visualize what the solution would be
(approximately 0.4), but am getting stuck at the analytical answer.
\!\(Plot[{Integrate[\@\((1 - x^2)\), {x, 0, s}], Pi/8}, {s, 0, 1}]\)
thanks
- sujai
--
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