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@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
–
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 $DG$ is a diameter.

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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TopNewestAre 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???

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$C$, $E$ and $H$ are respectively the midpoints of $AB$, $AC$, $DG$.

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

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$DG$ is a diameter.

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. AndLog in to reply