
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 23rd, 2019, 08:44 AM  #1 
Newbie Joined: Mar 2019 From: Coquitlam Posts: 1 Thanks: 0  The Area of the region of the Equilateral Triangle that lies Outside the Circle
I'm considering a circle of diameter D superimposed over the equilateral triangle of side length D, with their centres coinciding. What is the total area of the three regions of the triangle that lie outside the circle? 
March 23rd, 2019, 03:55 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,941 Thanks: 1545 
Hopefully, I interpreted your problem statement correctly. I looked at this problem to see if there was a way to calculate the desired area by means of elementary geometry. If there is, someone will no doubt point out a simpler method. Having failed any elementary method, I turned to using the calculus of polar graphs to determine it. I can tell you the exact solution is not nice as far as simplification is concerned. If you are interested, I determined the total area of the three small "triangular" looking regions to be ... $A = \dfrac{\pi+2(\sqrt{3}\sqrt{2})6\arctan\left(\frac{\sqrt{2}}{2}\right)}{8} \cdot D^2$ ... attached is a sketch of the diagram used. 

Tags 
area, circle, equilateral, lies, region, triangle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Equilateral Triangle in Circle  symmetry  Algebra  6  July 7th, 2015 12:57 PM 
Find the volume of the region that lies under the plane and over the triangle  kyliealana  Calculus  1  April 29th, 2015 06:12 AM 
Circumscribe an equilateral triangle around a circle  candi678  Algebra  1  January 27th, 2010 05:05 PM 
Equilateral Triangle and Circle  symmetry  Algebra  2  February 2nd, 2007 03:54 PM 
Circumscribe an equilateral triangle around a circle  candi678  Number Theory  1  December 31st, 1969 04:00 PM 