Inscribed Definition and 89 Threads

Homework Statement By employing spherical polar coordinates show that the circumference C of a circle of radius R inscribed on a sphere S^{2} obeys the inequality C<2\piR The Attempt at a Solution I proved C=2\piR\sqrt{1-\frac{R^2}{4r^2}} So if r>R, then the equality is correct. Am I right...

Homework Statement Ok, I wanted to calculate the sums of the areas of inscribed petagons into an initial pentagon (the smaller pentagon's vertices touch the larger pentagon's midpoints). However, I wanted all of the even pentagons to create negative space, and then the odd # pentagon after...

Homework Statement A large circle is inscribed with 3 smaller circles, eachhttps://www.physicsforums.com/newthread.php?do=newthread&f=156 of the four circles is tangent to the other three. If the radius of each of the smaller circles is a, find the area of the largest circle. Homework...

Ciao to everybody, I've encountered frequently, in forums and news groups, questions about a rectangle inscribed in another rectangle, but nowhere a general discussion on ways to solve related problems (i.e., given three of the five quantities involved - 2 sides of outer rectangle, 2 sides...

How do you determine if a point lies on the sides of a square inscribed on a circle ? I'm given only the radius of the circle and the circle is centered at the origin. My idea was to find the equation for each side and then to test the given point. However, I just realized that you can...

I'm looking for a formula that subtracts the area of an inscribed circle of a shape from the circumscribed area of the shape. I've confused myself on this one and can't seem to figure it out. The shape is a regular polygon (all sides and angles are equal). What should be given to "plug in" is...

Homework Statement The circle x2 + y2 - 4x - 4y + 4 = 0 is inscribed in a triangle, which has two of its sides along the coordinate axes. If the locus of the circumcentre is of the form x + y - xy + k(x2 + y2)1/2= 0. Find k.The Attempt at a Solution The centre of the given circle is (2,2) and...

I have an important paper to submit and I have a feeling I didn't solve the following correctly. I have to find the maximal volume of a Cuboid inscribed inside half of the Ellipsoid D={(x,y,z): x^2/a^2 + y^2/b^2 + z^2/c^2 <=1, z>=0 } So I decided to use Lagrange's multipliers. That's...

Find the area of the largest rectangle that can be inscribed (with sides parallel to the axes in the ellipse). x^2/a^2 +y^2/b^2 = 1 I came across the above problem and am not sure how to proceed with it. I drew the ellipse with the inscribed rectangle and tried repositioning the ellipse so...

ABC inscribed within a circle whose diameter AC forms one of the sides of hte triangle. If Arc BC on the circle subtends an angle of 40 ddegrees, find the measure of angle BCA within the triangle

Homework Statement Someone gave me this problem: finding the radius of the circle inscribed in the triangle with the given lengths. The Attempt at a Solution The person asking about this problem said it was taken from a beginning algebra textbook. I tried figuring it out using just...

Homework Statement Show that the square, when inscribed in a circle, has the largest area of all the 4-sided polygons. Try to show that all sides of a quadrilateral of maximal area have to be of equal length. The Attempt at a Solution How do you start? I don't get how showing the sides...

Let PQRS be a rectangle inscribed in a triangle ABC(i.e P is in AC, Q in BC and R,S are in AB). Find the locus of points that are intersection of diagonals of the rectangle. (i.e find the locus of intersection of RQ and PS)

Ive been out of school cause i was sick and am in geometry and got some of my work, its on inscribed angles in circles and since i missed the lecture i have no idea how to do it, I am not asking anyone to explain it to me cause i probly won't understand in words, but if anyone knows any videos...

Homework Statement Let ABC be a piece of a parabola. The point B is chosen such that the tangent to the parabola at B is parallel to the line AC. Archimedes proved the Area of parabola inside ABC is 4/3 times the triangle ABC. Prove this using calculus Homework Equations The integral...

Homework Statement Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed in the ellipse x^2 + 4y^2 = 4 Homework Equations The Attempt at a Solution I simplified the equation of the ellipse into the ellipse formula: x^2/4 + y^2 = 1...

1. The base of the yellow triangle has length 8 inches; its height is 10 inches. Each of the circles is tangent to each edge and each other circle that it touches. There are infinitely many circles. The radius of the largest of them is __________ and the total area of all the circles is...

Homework Statement Given the function y = 12- 3x^2, find the maximum semi-circular area bounded by the curve and the x-axis. Homework Equations A= Pi(r^2) The Attempt at a Solution I found my zeros, 2 and -2, and my maximum height of 12 from the y'. A' = 2Pi(r)

just out of curiosity - it seems evident to me that the capacitance of a conductive body should be between the capacitance of an inscribed sphere and the capacitance of a circumscribed sphere. But I can't figure out how to prove this. If you prove this, it follows that the energy required to...

In this diagram, a square is inscribed with four circles of equivalent size, all with the radius of 1. Each circle is tangent to two sides of the square, two circles, and the smaller circle. Obviously each side of the square is equal to 4, but what is the radius of the smaller circle? I...

Homework Statement A circle with radius 1 inscribed in the parabola y=x^2. Find the center of the circle.Homework Equations equation of the parabola: y=x^2 circle: (x-h)^2 + (y-k)^2 = 1 The Attempt at a Solution After ghosting the forums and reading through every post with this exact same...

For the next critical mass ride, I'm going to try to mount a gong inside the front triangle of my bicycle. Naturally, I want to maximize the radius of the gong and learn some geometry. I spent a couple minutes trying to derive it myself. The number of terms to take care of became huge, so I...

Is it true that the diagonals of a quadrilateral inscribed in a circle split the quadrilateral into two sets of similar triangles? Is yes, how do we prove this?

Homework Statement 2 identical circles of radius 5cm touching each other externally and both are touching an arc length of a larger 15cm circle. Find the 1. perimeter and 2. area of the region between the 2 smaller circles and the arc length of the larger circle Homework Equations s=r...

Homework Statement A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder. I'm just really confused on how to figure this one out. The equation for the volume of a cone is v = 1/3pi r^2h and the volume of a...

Homework Statement There is a semicircle with radius 1. Two circles are inscribe in it with centres C1 and C2 and radius r1 and r2 respectively. Find the maximum possible value of r1+r2 Here is the picture, I have drawn. http://img143.imageshack.us/img143/8392/circlesdn3.png The Attempt...

Homework Statement Largest possible area of a rectangle inscribed in the ellipse (x2/a2)+(y2/b2)=1 Homework Equations Area of the rectangle = length*height The Attempt at a Solution I have it set up so that the four corners of the rectangle are at (x,y) (-x,y) (-x,-y) (x,-y) and that...

[SOLVED] Optimization: Rectangle Inscribed in Triangle Homework Statement Please see http://www.jstor.org/pss/2686484 link. The problem I have is pretty much exactly the same as that dealt with in this excerpt. (focus on the bit with the heading "What is the biggest rectangle you can...

Find the area of the largest rectangle that can be inscribed in the region bounded by the parabola with equation y= 4 - x^2

Homework Statement Each edge of a square has length L. Prove that among all squares inscribed in the given square, the one of minimum area has edges of length \frac{1}{2}L\sqrt{2} Homework Equations The Attempt at a Solution I started by drawing a square of sides L. Then labeled...

A pyramid ABCDS is given (the base is convex quadrilateral). A sphere is inscribed in this pyramid and it is tangent to side ABCD at point P. Prove that \angle APB + \angle CPD = 180^{o}

Homework Statement Find the Perimeter of an equilateral triangle inscribed in a circle knowing the radius r. Homework Equations - The Attempt at a Solution Browsing the web I found that the intersection of the three perpendicular bisectors of a traingle is the center of it's...

The problem is to find the radius and height of the open right circular cylinder of largest surface area that can be inscribed in a sphere of radius a. What is the largest surface area? The open cylinder's surface area will be f(h,r) = 2 \pi r h I am not really sure about the sphere...

P is a point inside triangle ABC. In the triangle there is inscribed circle which radius is greater than 1. Prove that PA>2, PB>2 or PC>2. I don't know how to solve it. Could anybody help me?

Can anyone help me with this problem? Suppose a sphere is colored in two colors: 10% of the surface is white, and the remaining part is black. Prove that there is a cube inscribed in the sphere such that all vertices are black thanks ~matt

Hey ppl, Could anyone help me with this: what is the ratio of the areas of the circumscribed and inscribed circles of a regular hexagon? how do I go about working it out from first principles? Cheers, joe

I'm working on this problem. The only given information is the circle is inscribed into the triangle. And you have to find the radius of the circle. The answer is... \frac{2\sqrt{5}}{3} Can someone come up with an explanation as to why? It's been a few years since I had geometry...

"Hi, I have a question on max vol. q. Its invloved with multivariable calculus. Q) Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9x^2+36y^2 + 4z^2 = 36. What i did was i found the three x,y and z-intersection points...

A right circular cone is inscribed in a hemisphere. The figure is expanding in such a way that the combinded surface area of the hemisphere and its base is increasing at a constant rate of 18 in^2 per second. At what rate is the volume of the cone changing when the radius of the common base is 4 in?