consrtruct a geometric figure

lawrence shared this question 1 week ago
Answered

Need to put point D lie on line CE. (The control points are Q,Q' and B). Need neater and shorter method to construct the figure satisfying the given conditions in the question. Any help or advice is much appreciated. thanks

Best Answer
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Désolé , je n'avais pas vu cette contrainte .

Avec cette contrainte (CF=12) les ponts A , C , E et F sont cocycliques .

Comments (20)

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Bonjour ,

beta max =19°.45

Plusieurs possibilités .

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Thanks. But CF=AB-12 is the given condition which is not satisfied in the construction.

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Désolé , je n'avais pas vu cette contrainte .

Avec cette contrainte (CF=12) les ponts A , C , E et F sont cocycliques .

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les points A , C , E et F semblent cocycliques

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Finalement alpha = beta = 17.413092°

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Thanks so much!

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Please, could someone take into consideration the constraints of the given (and highly interesting) problem in order to find the geometric solution? Up to now, it seems that the solution is confined to successive approximations, as shown in attachments. Cheers

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Are you sure there is a geometric solution ?

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I hope so!

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In terms of Dynamic Geometry, as Geogebra belongs, the solution is given below (attachments) and can be considered satisfactory. Few words to say how is reached: circle radius BF=FG= sqrt(120)-6 = 4.95445, namely the positive root of equation (x^2+12x-84=0), and DF=3.9962, highly closed to 4. Cheers

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Si on accepte une solution algébrique et des outils comme GeoGebra , alors comme on a calculé BF = FG = 2 √2 √3 √5 - 6 on peut calculer AD car AD/AE = 4/FG

Soit AD = 20/FG et AF = AD + 4

Ainsi on peut construire le triangle ABF connaissant ses trois côtés

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Oh yes. Your refining, coming from point E belonging to one circle, is suitable to reach the solution as accurate as possible. Please, could you try to slightly modify your nice construction starting from side AB over xAxis? As I've done previously, in order to ease students' approach. Thanks

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Direct solution, starting from the known radius of circle, as follows

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Si AB reste sur l'axe des x , on ne peut déplacer le point E qui est sur AB .

Et déplacer un autre point (F ou C) donne des coïncidences moins précises

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Th above direct solution, coming later to my previous request, gives exact sides and angles values (without approximations I mean), so I'm satisfied for such a result. Thank you very much for your appreciated drifts and feedbacks. Cheers

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Autre construction (sans angles)

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Wow! So fine, this is really a good proposal for students' investigation. Thank you

P.S: att'd type mismatch

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thank you very much for having corrected my mistake

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In the attachment my solution (after a long time)

She is very similare to the solution of frndmrsl (without angles) with a other way for AD.

technical differences:

- using CAS

- sliders for variables

- construction is movable (A) and can be rotate (B)

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Very nice method of investigation, rami! Screenshot shows three positions of some points aligned. Cheers

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