Sounds difficult

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.

#Geometry #Polygons #Rectangle

Easy Math Editor

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.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Hint: Read this wiki.

Calvin Lin Staff - 6 years, 5 months ago

How is this going to help? We can just get the value of x, nothing else.

Agr Amul - 6 years, 5 months ago

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 - 6 years, 5 months ago

@Calvin Lin – Sir, does projection mean perpendicular? Well, I m not able to form equations.

Agr Amul - 6 years, 5 months ago

@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 - 6 years, 5 months ago

@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 - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$