# inscribed

1. ### Arcs Doubt in a circle.

Greetings, I'm having a discussion with my teacher, where we got to apply the theorems of the angle inscribed in the circumference. I don't know whether it's true that the following arc PE is equally to angle A, since we got the inscribed theorem where it should be the double of the angle A...
2. ### Limit of inscribed regular polygons

An equilateral triangle of side 1 is inscribed by the largest square possible which is inscribed by the largest regular pentagon possible, ad infinitum. What is the radius of the limiting circle?
3. ### Rectangle inscribed in a circle

Is the area of a rectangle inscribed in a circle ever rational?
4. ### Equilateral triangle inscribed into an ellipse

Hi everybody! I am a college student and I'm new here. I am struggling with this problem for a couple of days , so I decided to ask you guys for a help. Hope this is the right section for this thing. Given an ellipse and a point on it, is it always possible to find other two points so...
5. ### How to find a relationship between the elements in a circle inscribed in a triangle?

I'm stuck with this particular problem: It states the following: A circle is inscribed in a triangle whose $M$, $N$, and $Q$ are tangential points. The lengths of $CB=40$ and $AB=9$. $\textrm{Find CM-AN}$ First off, I must say the segment line notation is hard for me to understand...
6. ### Related rates - inscribed

A rectangle is inscribed in a semicircle of a radius 5m. Estimate the increase in the area of the rectangle using differentials if the length of its base along the diameter is increased from 6m to 6 1/6 m ?
7. ### Isn't every n-gon inscribed in a given circle constructible?

Can't you just construct a line that is 6 times the radius of the circle. Then n-sect the line and use the length of the section as the side length of your n-gon?
8. ### Maximum area of a square inscribed in a triangle

I'm really stumped on this problem. I have worked out the three smaller triangles inside of the bigger triangle but after that, nothing else at all.
9. ### inscribed circle of a triangle

Can anyone help me with this problem? I have no idea how to solve it. Thanx in advance!
10. ### Semicircle inscribed in trapezium

Hi so I'm stuck on another geometry problem: ABCD is a trapezium with a semicircle, centre O, inscribed in it.* If AO=OD, prove that (AO)(OD)=(AB)(CD). I've tried Pythagoras' theorem on the radius, and extending AB and CD to meet but neither of them work. I'd appreciate any hints. Thanks...
11. ### Pi Trapezium inscribed circle

With a small semicircle at the top and three semicircles equal in area around. Two horizontals and two diagonals. 3.1... For example Diagonals 1m 1m Horizontals 1m 1dm Just thought this would be cool, it might have some use, I don't know.
12. ### Can anyone help me? (inscribed squares)

Hi there! I am struggling with this problem, I am just not sure what to do! I had an idea for what to do for letter a, but I'm not sure about it. And if you could help with b too, that would be great!
13. ### Curves that couldn't be inscribed in rectangle

Problem: tourist get lost in the forest. Forest is rectangle with width = 1 and height >>> 1. So what curve will be the shortest universal way out? So in this problem we need to find shortest curve which couldn't be inscribed into rectangle. It seems to me that the shortest way is two of...
14. ### A cirlce inscribed inside a right triangle...

This is a 3-part question in my Calculus textbook, one of the challenge problems. I don't even think the part I'm having trouble with even requires calculus, but it's driving me nuts because I can't solve it. Here's the question: (circle is tangent at D) C |\...D |......\ |_______\B A Now...
15. ### Triangle inscribed in a circle problem

Hi, Could you please help with the solution or give the idea of it for the following problem: ABC triangle with sides AB=14, BC=13, AC=15 inscribed in a circle with a center in the point O. Point M dimidiates AB side. Point B' was chosen in the circle so that BB' goes through the point O...
16. ### Quadrilateral inscribed in a circle

Hello! ABCD quadrilateral inscribed in a circle of radius R,prove that: AB•BC•CD•DA<=4R^4 Thank you!
17. ### Largest possible inscribed triangle in a circle

Problem: "Show that the, in area, largest triangle of the in a circle inscribed triangles is an equilateral triangle. Guidance: First show that the equilateral triangle is the largest of the isosceles triangles." My first thought was to begin with defining the area of an inscribed isosceles...
18. ### circle inscribed inside parabolic sector

Here is a fun little problem. Not crazy difficult, but more like a contest problem. "A parabolic sector is bounded by y=-x^{2}+c and y=0. A circle of max area is inscribed in this sector. Find the radius of the circle in terms of c". Assume c\geq 1
19. ### Difficult problem: deltoid inscribed into an ellipse

I'm a math teacher and I've found a very hard problem in one of my math classrooms' textbooks. It was firstly proposed as problem n. 9, back in 1995, in the "Annual Iowa Collegiate Mathematics Competition". Link is http://mathcs.central.edu/MAA/contest/Problems/Probs95.htm (no solution file...
20. ### Sphere inscribed in pyramid

In SABCD pyramid, which is based on a convex quadrilateral ABCD, you can inscribe the sphere. Prove that : <) ASB + <) CSD = <) BSC + <) DSA