Homework is given to a child who is not ready for a math competition...

AA and BB are fixed points. Determine the locus of point II as DD moves on the perpendicular from AA to the segment ABAB. Please help me!

#Geometry

Note by Thành Đạt Lê
2 years, 5 months ago

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Comments

Are the points C and E also fixed???? Because, if they are, then how do you determine the position of G??? And is H the midpoint of DG???

Aaghaz Mahajan - 2 years, 5 months ago

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CC, EE and HH are respectively the midpoints of ABAB, ACAC, DGDG.

Thành Đạt Lê - 2 years, 5 months ago

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Okay.....but how do we define G???

Aaghaz Mahajan - 2 years, 5 months ago

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@Aaghaz Mahajan Is it the intersection of perpendicular bisector of DC and the line perpendicular to DB passing through E???

Aaghaz Mahajan - 2 years, 5 months ago

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@Aaghaz Mahajan Yup, it is.

Thành Đạt Lê - 2 years, 5 months ago

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@Thành Đạt Lê Ohhkay........coz, the picture was a bit misleading.....I assumed that DG is always parallel to AB, which isn't the case........

Aaghaz Mahajan - 2 years, 5 months ago

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@Aaghaz Mahajan You can prove that.

Thành Đạt Lê - 2 years, 5 months ago

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@Thành Đạt Lê Umm nope..........that isn't happening always........see my comment and my approach....you'll see what I mean

Aaghaz Mahajan - 2 years, 5 months ago

@Thành Đạt Lê But, I think the method I am using is lengthy...........What I am doing is, I have set up the Coordinate plane with the origin at C, then points A and B are (-2a,0) and (2a,0) and so, the point E becomes (-a,0)..........Now, we can give D the co-ordinates (-2a, 2y).........(Here, a is a real positive number, and y ranges.....).....Now, after some messy equation solving, I have the co-ordinates of G and H..........Here I have another doubt........Is I lying on the circle with DG as a diameter???

Aaghaz Mahajan - 2 years, 5 months ago

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@Aaghaz Mahajan Try to solve the problem. I already know the answer is a combination of half-parabola and a semicircle. But I don't know anything more specific. And DGDG is a diameter.

Thành Đạt Lê - 2 years, 5 months ago
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