# Geometry!!

Note by Shubham Bagrecha
5 years, 2 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. 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 1paragraph 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} $$\boxed{123}$$

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Everyone has assumed that a1 and area of other "similar looking" sectors are equal, so that 4a1 is their total area. Similar assumption have been made for a2 also. But one needs to prove these assumptions.

- 5 years, 2 months ago

Here is the another method. Though the answer is same but the reasoning involved in this method is such that one doesn't require the above stated two assumptions, so there is no need to prove the assumptions.$Area Of Sector SOQ = \frac {90}{360} \pi r^2$ $Area Of Semicircle STO = \frac {1}{2} \pi (\frac {r}{2})^2 = Area Of Semicircle QTO$ $Sector SOQ = a_1 + Semicircle STO + Semicircle QTO - a_2$ $\frac {1}{4} \pi r^2 = a_1 - a_2 + 2 \times (\frac {1}{2} \pi \frac {r^2}{4})$ $a_1 - a_2 = \frac {1}{4} \pi r^2 - \frac {1}{4} \pi r^2 = 0$

- 5 years, 2 months ago

0

- 5 years, 2 months ago

- 5 years, 2 months ago

4a1 + 4π(1/4)^2 - 4a2 = π(1)^2

- 5 years, 2 months ago

$$4a_1+4π(1/2)^2 - 4a_2 = π(1)^2$$, implies $$a_1 - a_2 = 0$$

- 5 years, 2 months ago

Comment deleted Apr 01, 2013

hey isn't 0 is the right answer? by using similarity??

- 5 years, 2 months ago