My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum

LinkBack Thread Tools Display Modes
May 15th, 2017, 07:16 PM   #1
Joined: May 2017
From: Buffalo NY

Posts: 2
Thanks: 0

Proving orthogonal circles

Starting from the circle and the point A as in the previous part, we construct Q as before, and then construct the line l through Q perpendicular to OA. Show that for any point P on l, the circle with center P and radius PA is orthogonal to the original circle. Please see the attached image to view figure
[Previous problem says the following (may or may not be helpful): Given a circle with center O and a point A is not the same as O inside the circle, we construct the line perpendicular to OA at A and denote by X one of the intersections of that line with the circle. The tangent line to the circle at X then intersects OA at point C. We let Q be the midpoint of AC.]
Attached Images
File Type: jpg Circle-min.jpg (13.4 KB, 1 views)
positron96 is offline  
May 20th, 2017, 05:08 AM   #2
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 895

Look at this:

(It doesn't help to post the same thing three times!)
Country Boy is offline  
May 22nd, 2017, 09:23 AM   #3
Joined: Jan 2016
From: Athens, OH

Posts: 92
Thanks: 47

As Country Boy suggests, this is easily solved with inversion with respect to a circle. Here's the diagram and solution that relies on a simple theorem:

johng40 is offline  

  My Math Forum > High School Math Forum > Geometry

circles, euclidean geometry, orthogonal, proving

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
RiDo Circles. Sin & Cos Circles RiDo Algebra 2 June 21st, 2012 02:31 AM
Proving integral with integrands f(x) and g(x) is orthogonal 1bh Calculus 2 June 16th, 2009 08:17 AM

Copyright © 2019 My Math Forum. All rights reserved.