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 June 3rd, 2019, 01:31 AM #1 Newbie   Joined: May 2019 From: Australia Posts: 8 Thanks: 0 The height of a section of overlapping circles. Say I have two identical circles, both of radii of one, overlapping, as shown in the diagram below: In this diagram, x is the circumference of the circles, and the bit of the bottom circle which is drawn blue (the overlapping bit) is 1/6th of the whole circumference. What I'm looking for is y, which is this: Now, working out x is easy - it's 2 \pi r, thus the overlapping bit is 1/3 \pi r. But how do I proceed in finding y from here? Help is much appreciated! Thanks! June 3rd, 2019, 04:48 AM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,981 Thanks: 1164 Math Focus: Elementary mathematics and beyond Imagine a right triangle from the centre of a circle, the midpoint of the segment y and one of the points of intersection of the circles. This triangle has hypotenuse 1 and side opposite the centre of the circle 1/2. Also, this triangle is 30-60-90. Can you use some basic trig and the Pythagorean theorem to find y? June 3rd, 2019, 05:11 AM   #3
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 Originally Posted by greg1313 Imagine a right triangle from the centre of a circle, the midpoint of the segment y and one of the points of intersection of the circles. This triangle has hypotenuse 1 and side opposite the centre of the circle 1/2. Also, this triangle is 30-60-90. Can you use some basic trig and the Pythagorean theorem to find y?
Although I know of trigonometry and Pythagoras, I don't see how having a point of the triangle at the midpoint of y can help me find the whole of y. June 3rd, 2019, 12:00 PM #4 Global Moderator   Joined: Dec 2006 Posts: 21,124 Thanks: 2332 Can you post a diagram with the suggested triangle shown? Certain lines are radii, so they have length 1. June 4th, 2019, 09:40 AM #5 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,981 Thanks: 1164 Math Focus: Elementary mathematics and beyond $\displaystyle \frac{y}{2}=1-\cos30=1-\frac{\sqrt3}{2}=\frac{2-\sqrt3}{2}\implies y=2-\sqrt3$ Tags circles, height, overlapping, section Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post edwardholmes91 Geometry 3 April 9th, 2018 09:04 AM nikkibunny Geometry 2 November 13th, 2016 11:22 PM math93 Geometry 0 November 3rd, 2015 03:43 PM Scrooge2013 Probability and Statistics 0 July 11th, 2014 12:55 PM rockey191 Algebra 2 July 3rd, 2009 03:08 AM

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