My Math Forum Largest possible inscribed triangle in a circle

 Calculus Calculus Math Forum

October 25th, 2013, 01:04 PM   #11
Senior Member

Joined: Jun 2013
From: London, England

Posts: 1,316
Thanks: 116

Re: Largest possible inscribed triangle in a circle

Quote:
 Originally Posted by Daltohn Since we're on the topic of optimization, how do you determine the largest value the expression (3x+4y) can take, when you have the constraint x^2+y^2=14x+6y+6 for the coordinates (x,y)? The answer is 73, I can get that using substitution and then the derivative or Lagrange Multipliers. But how do you determine that without any calculus at all? Is there some trick since the constraint is a circle? It's a problem from a while back, when we hadn't done any calculus.
One method is to substitute w = x - 7 and z = y - 3, then (w, z) lies on a circle centre (0,0) with radius 8. And, switching to polar coordinates, w = 8cos(a) and z = 8sin(a).

So we have to maximise 24cos(a) + 32sin(a) + 33.

$24cos(a) + 32sin(a)= \sqrt{24^2 + 32^2}cos(a+\beta) \ where \ \beta = tan^{-1}(\frac{-4}{3})$

This has a maximum of 40, hence the maximum of the function is 73.

 October 27th, 2013, 09:19 AM #12 Member   Joined: Oct 2013 Posts: 31 Thanks: 0 Re: Largest possible inscribed triangle in a circle Thanks a lot for your help, everyone!

 Tags circle, inscribed, largest, triangle

,
,

,

,

,

,

,

,

,

,

,

,

,

,

# max area of triangle inscribed in circle

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post galactus Calculus 5 September 3rd, 2015 02:45 PM Ionika Algebra 4 April 13th, 2014 04:05 PM elim Algebra 5 January 22nd, 2011 08:36 AM graviton120 Algebra 6 July 25th, 2009 04:16 AM Daltohn Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top