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October 13th, 2018, 05:19 AM  #1 
Member Joined: Sep 2017 From: Saudi Arabia Posts: 37 Thanks: 1  Probability  Geometry of circles
Hi everyone, Can anyone help me for how to start solving the following problem? A triangle is to be formed by randomly choosing three distinct points on the circumference of a circle. What is the probability that this triangle is an acute triangle? Thanks Last edited by skipjack; October 13th, 2018 at 10:10 PM. 
October 13th, 2018, 02:08 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,885 Thanks: 1088 Math Focus: Elementary mathematics and beyond  
October 14th, 2018, 01:03 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,986 Thanks: 1853 
The three points divide the circumference of the circle into three arcs that don't overlap. Consider what property the lengths of these arcs possess if and only if the triangle is acute. Restate the problem in terms of straight lines of the same lengths as those arcs. Read about Viviani's theorem. Now read this article and answer the question given in the last paragraph of that article. If you're still stuck, try doing a web search using search terms suggested by the above links. 
October 17th, 2018, 05:43 AM  #4  
Senior Member Joined: Oct 2013 From: New York, USA Posts: 623 Thanks: 85  Quote:
 

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