Waste less time on Facebook — follow Brilliant.
×

Question from IMO

A hoop is resting vertically at stair case as shown in the diagram.AB=12cm and BC=8cm. The radius of the hoop is..

Note by Neha Adepu
4 years, 1 month ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. 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"
MathAppears 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

Sort by:

Top Newest

If you make a center point, let's call it O, then you know that OA=OC (both radii). If you extend the line of the stair (the one parallel to the ground) out horizontally, it will eventually intersect OA. Label this point of intersection D. Now you have formed a right triangle (triangle ODC). You know that BC=AD=8. Therefore OD=OA-AD=OA-8. You also know that AB=DC=12. Using the Pythagorean theorem, you can determine the length of OC. (OA-8)^{2}+12^{2}=OC^{2}. OA^{2}-18OA+64+144 =OC^{2}. OA^{2]-18OA+208=OC^{2}. Since OC=OA (both radii), we can plug in OA for OC. OA^{2}-18OA+208=OA^{2}. Then it is merely algebra. -18OA+208=0. 18OA=208. OA=208/18. OA=104/9.

Michael Thew - 4 years, 1 month ago

Log in to reply

You have everything up to the Pythagorean theorem right. You messed up here: \[(OA-8)^{2}+12^{2}=OC^{2}\] \[OA^{2}-18OA+64+144 =OC^{2}\]

The \(-18OA\) should be \(-16OA\). This gives the correct answer \(OA=13\).

Daniel Chiu - 4 years, 1 month ago

Log in to reply

Thank you for the correct answer!

Neha Adepu - 4 years, 1 month ago

Log in to reply

Thanks a lot! It was of great help!

Neha Adepu - 4 years, 1 month ago

Log in to reply

Fuck offffff

Vinit Kumar - 10 months, 4 weeks ago

Log in to reply

O thanks Daniel. I was wondering why it was such a messy fraction.

Michael Thew - 4 years, 1 month ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...