My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Thanks Tree4Thanks
  • 1 Post By greg1313
  • 3 Post By skipjack
Reply
 
LinkBack Thread Tools Display Modes
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.
Hussain2629 is offline  
 
October 13th, 2018, 02:08 PM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,885
Thanks: 1088

Math Focus: Elementary mathematics and beyond
See this page.
Thanks from topsquark
greg1313 is offline  
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.
Thanks from greg1313, topsquark and Hussain2629
skipjack is offline  
October 17th, 2018, 05:43 AM   #4
Senior Member
 
Joined: Oct 2013
From: New York, USA

Posts: 623
Thanks: 85

Quote:
Originally Posted by skipjack View Post
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.
EvanJ is offline  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
circles, geometry, probability



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
How do you show a Möbius transformation maps circles to circles and lines? math93 Geometry 0 November 3rd, 2015 03:43 PM
geometry (circles) rahul gupta Geometry 1 December 24th, 2013 10:34 PM
Geometry - Circles in Rectangle Zofaan Geometry 6 December 17th, 2011 05:17 PM
Geometry : Circles and Squares rnck Geometry 2 November 27th, 2011 05:41 AM
Geometry - Circles in Rectangle Zofaan Math Events 1 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.