# Perpendicular Chords of a Circle

Help Required: Given a point P in the interior of a circle of radius 1 unit with two perpendicular chords through P and another pair of perpendicular chords through P that make an angle of θ radians with the first pair, as shown in the figure, find the area of the shaded region.

Note by One Top
2 years, 3 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} $$\boxed{123}$$

Sort by:

Hint: As suggested by the problem, the answer is independent of the point (as long as it's contained within).

Now, figure out how to prove this fact.

In particular, what can we say about how the circumference is split into these regions?

Staff - 2 years, 3 months ago

I don't understand can you help me?

- 2 years, 3 months ago

We can consider specific cases and conclude that the answer is 2θ but so far I have not been able to prove it for any general point within the circle. Would 2θ be correct?

- 2 years, 3 months ago

Yes, that conjecture is correct.

Staff - 2 years, 3 months ago