Triangle Optimization problem

  • Thread starter ptolema
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  • #1
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Homework Statement



A right angle is moved along the diameter of a circle of radius a (see diagram). What is the greatest possible length (A+B) intercepted on it by the circle.

fig27.jpg


Homework Equations



so, the pythagorean theorem might be useful
diameter = 2a

The Attempt at a Solution



i have to maximise A+B, but i don't exactly have an equation to do that. maybe maximising A2+B2 would work, but that still leaves me with too many variables. i don't know how to relate anything from the circle to the right angle besides the obvious diameter. i know that 0<A<a and 0<B<2a, but this once again gets me nowhere. no idea where to start, please help!
 

Answers and Replies

  • #2
tiny-tim
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Homework Helper
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hi ptolema! :smile:

hint: draw the line from A to the centre of the circle, and call the angle there θ. :wink:
 
  • #3
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thanks, that was a big help!
 

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