MHB Radius Small Circle: Measurement & More

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Circle Radius
AI Thread Summary
The discussion focuses on calculating the radius of a small circle inscribed within a square with a side length of 2. Using the Pythagorean theorem, the relationship between the radius (x) and the square's dimensions is established through the equation (1-x)² + 1 = (1+x)². Solving this equation reveals that the radius x equals 1/4. The solution is confirmed as correct and well-received by participants. The mathematical approach effectively demonstrates the application of Pythagorean theorem in geometric contexts.
Albert1
Messages
1,221
Reaction score
0

Attachments

  • radius of small circle.jpg
    radius of small circle.jpg
    25.8 KB · Views: 102
Mathematics news on Phys.org
[sp]Let suppose that the side of the square is 2. In this case, if x is the radius of the 'small circle', for the theorem of Pythagoras it must be...

$\displaystyle (1-x)^{2} + 1 = (1+x)^{2}$

... so that is $\displaystyle x = \frac{1}{4}$...[/sp]

Kind regards

$\chi$ $\sigma$
 
hint:
see Ford Circles
 
chisigma said:
[sp]Let suppose that the side of the square is 2. In this case, if x is the radius of the 'small circle', for the theorem of Pythagoras it must be...

$\displaystyle (1-x)^{2} + 1 = (1+x)^{2}$

... so that is $\displaystyle x = \frac{1}{4}$...[/sp]

Kind regards

$\chi$ $\sigma$
very good solution !
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

MHB Calculate the radius of the circle
Replies
5
Views
2K
I Is the Ratio of Circumference to Radius of a Circle Always Irrational?
Replies
19
Views
3K
B Why does the radius of a unit circle need to be 1?
Replies
36
Views
5K
MHB Relationship between inner and outer radius of a two concentric circles
Replies
2
Views
2K
MHB Area of multiple circles inside a rectangle
Replies
3
Views
2K
B Circle tangent to two lines and another circle
Replies
2
Views
3K
B Understanding why πr^2 works for different area calculations
Replies
7
Views
2K
B Strange Relationships of the Circle
Replies
10
Views
2K
B Do I have enough information to find the radius?
Replies
16
Views
2K
B How to find a length of a "radius" not centered in a circle?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top