My Math Forum Probability | Geometry of circles
 User Name Remember Me? Password

 Probability and Statistics Basic Probability and Statistics Math Forum

 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: 7,913 Thanks: 1113 Math Focus: Elementary mathematics and beyond Thanks from topsquark
 October 14th, 2018, 01:03 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,302 Thanks: 1974 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. Thanks from greg1313, topsquark and Hussain2629
October 17th, 2018, 05:43 AM   #4
Senior Member

Joined: Oct 2013
From: New York, USA

Posts: 635
Thanks: 85

Quote:
 Originally Posted by skipjack 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.
The sum of the distances from a point in an equilateral triangle to the sides equaling the altitude is something I understand easily. For the broken stick problem, tell me if this explanation is correct. Take a length of 6 broken into 3 parts. There is a 3/4 probability that the longest part will be greater than 3, in which case the parts cannot form a triangle, and a 1/4 probability that the longest part will be between 2 and 3. Neither of those helps me solve the original problem.

 Tags circles, geometry, probability

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post math93 Geometry 0 November 3rd, 2015 03:43 PM rahul gupta Geometry 1 December 24th, 2013 10:34 PM Zofaan Geometry 6 December 17th, 2011 05:17 PM rnck Geometry 2 November 27th, 2011 05:41 AM Zofaan Math Events 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.