Circles in an equilateral triangle.

AI Thread Summary
The discussion revolves around finding the ratio of the area of three circles, each tangent to the vertices of an equilateral triangle, to the area of the triangle itself. Participants clarify the initial confusion regarding the placement of circles and triangles, with the correct interpretation being that three circles are inscribed within one triangle. The relevant formulas for calculating the areas of circles and triangles are provided, including the area of a triangle using its base and height. Despite attempts to solve the problem using various methods, participants express difficulty in making the necessary logical connections. The conversation highlights the need for clearer problem statements to facilitate understanding and solutions.
Synxervious
Messages
10
Reaction score
0

Homework Statement



Three triangles are placed into a circle; The vertices of the triangle are tangential to each circle. How do you find the ratio of the area of the circles to that of the triangle?

Homework Equations



pi r^2, 1/2(b)(h), sqrt3/4 * a^2 (2r^2).

The Attempt at a Solution



Tried drawing lines within, tried using double angle formulae, tried a lot of different things, but I still can't make that logical jump. Help? :(
 
Physics news on Phys.org
"Three triangles are placed into a circle; The vertices of the triangle are tangential to each circle. How do you find the ratio of the area of the circles to that of the triangle?"

Your first sentence implies there is only one circle and three triangles. The question implies there is more than one circle but only one triangle. It sounds a bit vague to me.
 
Whoops sorry. I meant.

"Three circles are placed into a triangle.". That's it. LOL
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Triangle inscribed in a circle
Replies
16
Views
3K
Perimeter/Area of Shaded Region within a Circle
Replies
10
Views
24K
Finding area of a non right angled triangle
Replies
9
Views
3K
{Geometry} Find length of the equilateral triangle
Replies
7
Views
2K
Area of interior triangle of pyramid normal to a side length
Replies
3
Views
2K
How Do Three Tangents Form an Equilateral Triangle Around a Circle?
Replies
7
Views
3K
Portion of Altitude of a Triangle Inscribed in a Circle
Replies
9
Views
4K
Find the third coordinate of a vertex of an equilateral triangle
Replies
11
Views
10K
Find the limit of the sum of the areas of all these triangles
Replies
7
Views
1K
A geometry problem with a circle and a bisected radius
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top