_ B __*** | AB__*** | __*** |BC __*** _| _*_______________________|_| A C? I need to find C given A, B, AB and BC

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# Finding coordinates of unkown point in right angle triangle

Started by jack_1313, Feb 14 2007 10:21 PM

5 replies to this topic

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#1
Members - Reputation: **536**

Posted 14 February 2007 - 10:21 PM

Hello.
I’m trying to find the coordinates of an unknown point © in a right angled triangle. Allow me to attempt to demonstrate:
I know the points A and B and therefore know the length of the side connecting them (AB). I also know the length of BC and that there is a right angle at point C. Finding the length of AC using Pythagoras and the unknown angles using trigonometry is trivial. The problem is that I do not know how to find the coordinates of point C efficiently.
I already know I can test a circle centred on the midpoint of AB, diameter equal to that sides length, with a circle centred on B, radius equal to the length of BC. I’d prefer to avoid doing this though as it seems like an overkill, and I am hoping for the fastest method as this calculation will be a vital part of a path finding routine and will be called upon hundreds of times in one search (the true problem is finding a tangent to a circle that runs through a given point).
Thanks for any help,
Jackson Allan.

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#4
Banned - Reputation: **794**

Posted 14 February 2007 - 11:04 PM

This is a link to a site that details the general solution for the intersection of two circles. Using equation (5) you can work out the point on AB where a line perpendicular to AB passes through C. Equation (7) gives the distance along the perpendicular to C. Note that there are two solutions.

Skizz

Skizz

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#5
Members - Reputation: **536**

Posted 14 February 2007 - 11:17 PM

Thank's for that, but the intersecting circles method is the one I'm already using to solve this problem. I was hoping their would be a method that performs quicker (not involving several square roots).

Edit: I'm having a good read through the link now, please excuse me if I've dismissed it prematurely.

Edit: I'm having a good read through the link now, please excuse me if I've dismissed it prematurely.