<![CDATA[Constraint on a length of a triangle's side]]>
https://help.geogebra.org/topic/constraint-on-a-length-of-a-triangles-side
Thu, 05 Nov 2020 11:29:02 +0000Mon, 02 Nov 2020 20:45:00 +0000Zend_Feed<![CDATA[Ce n'est pas toujours possible d'obtenir un tel triangle Utiliser 2 cercles s'ils sont sécants, c'est gagné]]>
https://help.geogebra.org/topic/constraint-on-a-length-of-a-triangles-side#comment-291850
Mon, 02 Nov 2020 21:14:22 +0000<![CDATA[perhaps you can begin with B C and do A in a ellipse doing AB+AC=3BC]]>
https://help.geogebra.org/topic/constraint-on-a-length-of-a-triangles-side#comment-291852
Mon, 02 Nov 2020 21:56:17 +0000<![CDATA[or find all the points C with locusequation()]]>
https://help.geogebra.org/topic/constraint-on-a-length-of-a-triangles-side#comment-291854
Mon, 02 Nov 2020 21:53:03 +0000<![CDATA[That's very elegant. I will take a few moments and try to understand better what you've done here. Thanks a lot!]]>
https://help.geogebra.org/topic/constraint-on-a-length-of-a-triangles-side#comment-291876
Tue, 03 Nov 2020 09:33:11 +0000<![CDATA[If AC is fixed and you want to locate B we can work from mathmagic's ellipse. When A meets the minor axis, AC = 3/2 BC = AB. When A meets the major axis (on the left), AC = 2 BC and AB = BC. When A is between these two positions, i.e. in the top left quadrant of the ellipse let AC = (3/2 + x)BC = (3+2x)/2 BC where x is between 0 and 1/2. Then AB = (3/2 - x)BC = (3-2x)/2 BC. Solving for BC we get BC = (2/(3+2x))AC and BC = (2/(3-2x))AB. Equating these and solving for AB we get AB = ((3-2x)/(3+2x))AC. Now we know the distance of B from A and from C in terms of x so we can construct two intersecting circles centred at A and at C to locate B. In the scenario above, AC > AB. If we consider when A is in the top right quadrant then AC < AB. By doing a similar analysis we find BC = (2/(3-2x))AC and AB = ((3+2x)/(3-2x))AC. So for each x we get two locations for B.]]>
https://help.geogebra.org/topic/constraint-on-a-length-of-a-triangles-side#comment-291946
Wed, 04 Nov 2020 13:59:32 +0000<![CDATA[File attached.]]>
https://help.geogebra.org/topic/constraint-on-a-length-of-a-triangles-side#comment-291994
Thu, 05 Nov 2020 11:29:03 +0000