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In a rectangle ABCD, O is any pt. inside it and its distance from the 4 corners is as shown in fig. Then find the sides of the rectangle.

Note by Agr Amul
2 years, 4 months ago

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Hint: Read this wiki. Calvin Lin Staff · 2 years, 4 months ago

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@Calvin Lin How is this going to help? We can just get the value of x, nothing else. Agr Amul · 2 years, 4 months ago

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@Agr Amul Great, that's a start. What can we do next?

If X, Y are the projections of O onto AB, BC, can we find AX, XB, BY, YC? Calvin Lin Staff · 2 years, 4 months ago

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@Calvin Lin Sir, does projection mean perpendicular? Well, I m not able to form equations. Agr Amul · 2 years, 4 months ago

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@Agr Amul Yes. "The Projection of P onto AB is X" means "Drop a perpendicular from P to AB, intersecting AB at X".

Write out the equations of Pythagorean theorem. For example, \( XB^2 + BY^2 = OB^2 \). You should have 4 equations. Does that help you solve for the sides? Why, or why not?

Note: I am not claiming that there is a unique set of solutions. I'm merely guiding you down what is the next sensible / logical step to take. It is not guaranteed that this must lead to a solution. Calvin Lin Staff · 2 years, 4 months ago

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@Calvin Lin This, initially i thought would help; but its not doing any good to this question. Kindly suggest me something else, sir. Agr Amul · 2 years, 4 months ago

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