# Tagged Questions

For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

1answer
22 views

### Permutations of geometric structure

Sorry about the title, i don't know how to describe this problem. I tried counting my way through this problem but kept getting the wrong answer(which is 12, by the way). Is there a more systematic ...
0answers
10 views

2answers
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### What is this question asking for exactly?

So I'm given a question that asks: "A coffee filter is cone shaped with radius = 4 and height of 8. Suppose filter is filled with water up to a height of level h. Find an expression for the volume of ...
0answers
22 views

### Criterion for an affine isomorphism.

I am reading Don Taylor's book 'The Geometry of Classical Groups' and currently I am trying to understand the affine geometry section. There is a lemma which appears to be a criterion for a bijection ...
2answers
36 views

### Why can't I know if the figure is a rectangle, if angles c+d=180 and c=d?

I have a four sided figure, abcd (see the image, and ignore the EF part), where I know that angles c+d=180 and c=d. However, this isn't enough information to decide if this is a rectangle - why is ...
0answers
8 views

2answers
64 views

### Finding area of a part of a circle

I have the values of $L$, $R$ and $W$ in the picture below. The circle is drawn though the center of the rectangle. And the circle will always intersect the rectangle. How can I find the area of the ...
3answers
54 views

### How to find the area of the following isosceles triangle

I am stuck with the following problem : What is the area of an isosceles triangle whose equal sides are $20$ cm and the angle between them is $30^{\circ}$ ? It is a nineth standard problem and ...
0answers
6 views

### Fisheye equidistant projection mapping to fisheye stereographic projection?

I have a set of images captured by a wide-angle (fisheye) lens camera, and the projection is linear-scaled (equidistant). I would like to remap from this projection to fisheye stereographic, which is ...
0answers
36 views

### Geometric Description Of a Set In The Complex Plane

$$S_1=\left\{z:Im\left(\frac{z-z_1}{z-z_2}\right)=0, z_1,z_2 \in \Bbb C\right\}$$ $$S_2=\left\{z:Re\left(\frac{z-z_1}{z-z_2}\right)=0, z_1,z_2 \in \Bbb C\right\}$$ Can someone help me with the ...
0answers
40 views

### Division of a square and value of a disk

I cam across this problem and I really don't know how to solve it. So you start with a square that has value 1. You divide this square in 4 so that each new square has a new value, as given by the ...
1answer
3 views

### Find intersecting points on rectangle edges for line drawn inside it

Draw a rectangle ABCD. Draw a line inside it connecting any two edges GF. Draw a perpendicular bisector to line GF. At what points does the perpendicular bisector intersect the edges of the ...
0answers
25 views

### A generalization of the Sawayama lemma

Let $ABC$ be a triangle, let $D$ be a point on the line $BC$. The Thebault circle is a circle tangent $AD, BC$ and the circumcircle (yeallow circles in the following figure). I give a ...
1answer
54 views

### The function of distance between two points with time

Consider I have two points p and q, and a line segment l: y=mx+c (actually the enpoints of the segment are given). There is a circle with center q which is growing with time t, i.e. the radius r = k.t ...
1answer
35 views

### Shortest possible distance to locate an unknown road

You are stranded in the middle of a large desert and the only way home is a through a straight road, which unfortunately you do not know the location of. If the perpendicular distance from you to ...
1answer
43 views

### Prove that the Area of triangle whose vertices are $(0,0)$, $(b,a)$ and $(x,y)$ is $|by-ax|/2$

Prove that the Are of triangle whose vertices are $(0,0)$, $(b,a)$ and $(x,y)$ is $\displaystyle \frac{|by-ax|}{2}$. I found this problem in Number theory by George Andrews, but I wonder how it ...
0answers
16 views

### Intersection of Circles and Triangulation [on hold]

Tracking a Cellphone CT1 to CT2 = 700m CT2 to CT3 = 1200m CT1 to CT3 = 1350m Cell Phone is 600m from CT1, 650m from CT2, and 800m from CT3 Draw a circle in each Cell Tower, indicating the distance ...
1answer
42 views

### Show that three circles are coaxal

Let $A_1, A_2, A_3, A_4$ are collinear, $B_1, B_2, B_3, B_4$ are collinear. Such that $A_1, A_2, B_2, B_1$ lie on circle $(O_1)$, and $A_3, A_4, B_4, B_3$ lie on circle $(O_2)$. Let $MNPQ$ be the ...
0answers
26 views

### Proof of the Isoperimetric Theorem in Higher Dimensions

I have read a couple of nice proofs for the isoperimetric theorem in 2 dimensions. Is there a simple proof for the isoperimetric theorem in $n$ dimensions? In other words, how do you prove that the $n$...
1answer
15 views

### Forming a expression of quadratic equation involving polygons

Six congruent isosceles triangles with equal sides $x$ cm are removed from the six corners of a paper in the shape of a regular hexagon of sides 20cm . The remaining portion is in the shoe of a 12 ...
1answer
47 views