0
votes
3answers
51 views

Equation of a line passing through a given point, perpendicular with a line [closed]

I need the equation of the line passing through a given point $A(2,3,1)$ perpendicular to the given line $$ \frac{x+1}{2}= \frac{y}{-1} = \frac{z-2}{3}. $$ I think there must bee some kind of rule ...
0
votes
3answers
67 views

Perpendicular lines inside and outside a circle

No trigonometry allowed. Let $\Delta ABC$ be inscribed inside a circle.Let $P$ be a point on the circle.Let $PD$ and $PE$ be perpendiculars on on $BC$ and $AC$ respectively.Let $DE$ when extended ...
0
votes
2answers
84 views

Solve the following problem…

My problem is: In a circle of radius $R$ is inscribed an equilateral triangle $ABC$. Through the point $C$ is drawn a line which intersects $AB$ in point $M$ and the circle, for the second time, in ...
1
vote
0answers
31 views

Solution for the value of an angle of a triangle ABC

Find value of angle m< DBC Where $$BD=DC=AC$$ $$2(m\langle BAC)=14(m\langle ABD)=7(m\langle BCD)$$ I tried hard but im out of ideas now, I know the answer is 20 but I want to know how, thanks ...
-3
votes
1answer
29 views

what is the X coordinate of point with Θ-90 degree [closed]

what is the X coordinate of point with Θ-90 degree ? 1- 0 2- 1.414 3- 7.07 4- infinity if I used this x = r sin(Θ)cos(ϕ) how can start I mean that if I substitution with Θ in sin with Θ-90 ...
0
votes
1answer
17 views

what is the X component of the point , where the spherical coordinates of point are (100,30,60)?

The spherical coordinates of point are $(100,30,60)$, what is the X component of the point $30$ $43.3$ $50$ $75$ I know that in the spherical coordinates, $$x = r \sin(\theta) \cos(\phi),$$ so ...
0
votes
1answer
35 views

spherical coordinates

spherical coordinates of point are $(10,20,30)$, the distance between the point and the origin of coordinate system is ? 1- $10$ 2- $14.4$ 3- $20$ 4- $30$ I know that the distance between two ...
0
votes
0answers
27 views

In the change-of-variables theorem, must $ϕ$ be globally injective?

In the above theorem, doesn't $\phi$ need to be injective too? The inverse function theorem merely implies that $\phi$ is locally injective -- is this sufficient? I ask because Marsden, in his ...
-1
votes
1answer
80 views

Ratios involving altitudes in a triangle [closed]

Consider a triangle ABC with an arbitrary point M inside it, while MB" , MC" , MA" are distances and AA' , BB' , CC' are heights of the ABC triangle. I need to prove the following: ...
0
votes
0answers
81 views

Points in the interior of an angle

I would like some help for the following question about proving that a point is in the interior of an angle (it involves betweenness of rays too): Prove that if ray BA - ray BC - ray BD and point P ...
-4
votes
2answers
1k views

Two points: Distance, midpoint, equations of line passing through them and perpendicular line [closed]

Consider two points (-2,3) and (-1,6). Calculate the distance between these two points. Find the midpoint. Obtain the equation of the line passing through the given points. Find the equation of the ...
2
votes
2answers
63 views

Length of Chord is Independent of Point P

This is question 1.49 from Baragar's textbook called A Survey of Classical and Modern Geometries if anybody is familiar with that text. This question is assigned as homework, so I am just looking for ...
1
vote
2answers
124 views

An inconstructible quadrilateral

A student tried to draw a quadrilateral $STOP$ with $ST=5cm$, $TO=4cm$, $\angle S = 20^{\circ}, \angle T = 30^{\circ}, \angle O = 40^{\circ}$. But he found out that it was impossible to construct ...
3
votes
2answers
100 views

Distance between $3\times3$ matrices (isometries)

The problem is pretty long, so I'm going to describe it while writting what I have so far. First I have to asociate the $3\times3$ matrices with $\Bbb R^9$, so we defined $\phi:M_{3\times3}(\Bbb R) ...
2
votes
1answer
81 views

Plane isometries $g\ , f$ , properties of fixed points and types

Given two plane isometries $g\ , f$ and $f^{'} = g\circ f \circ g^{-1}$ prove that: If $P$ is a fixed point of $f$ then $g\left(P\right)$ is a fixed point of $f^{'}$ and if $Q$ is a fixed point of ...
0
votes
2answers
28 views

What is the ratio of the perimeter of $OPRQ$ to the perimeter of $OPSQ$?

Area of circle $O$ is $64\pi$. What is ratio of the perimeter of $OPRQ$ to that of $OPSQ$ ($\pi = 3$)? Okay i have tried couple of things but seems its not working . Please suggest me proper ...
7
votes
1answer
530 views

Sum of distances from triangle vertices to interior point is less than perimeter?

Let $M$ be a point in the interior of triangle $ABC$ in the plane. Prove $AM+BM+CM<AB+BC+CA$. The above question was posed to someone I know who is taking high-school Euclidean geometry. I'm ...
2
votes
1answer
84 views

3D Geometry Question

In $3$-dimensional Geometry, if angle made of line segment $OP$ with $X,Y,Z$-axis are in $1:2:3$, then what is the angle made by line segment with $Y$-axis? My Solution: Let $\alpha,\beta$ and ...
0
votes
1answer
78 views

Problem on hyperbolic hyperboloid generated by a rotation

This is the problem: In $\mathbb{E}^3$ we consider the conic $\gamma$ of equations $x=yz-2=0$ , the line $a$ of equations $x=y+z=0$ and the surface $Q$, that is generated by the rotation of $\gamma$ ...
1
vote
2answers
179 views

A question on Trigonometry (bisector)

If two bisector of a triangular is equal, then it is Isosceles triangular.
2
votes
1answer
134 views

prove that the sphere with a hair in $IR^{3}$ is not locally Euclidean at q. Hence it cannot be a topological manifold.

A fundamental theorem of topology, the theorem on invariance of dimension, states that if two nonempty open sets $U ⊂ R_{n}$ and $V ⊂ R_{m}$ are homeomorphic, then n = m. prove that the sphere with a ...
1
vote
2answers
4k views

coordinate geometry: finding the ratio in which a line segment is divided by a line

The question is: Determine the ratio in which the line 3x + 4y - 9 = 0divides the line segment joining the points ...
12
votes
2answers
310 views

6 point lying on a common circle

$Z$ is an interior point of segment $XY$. Three semicircles are drawn over segments $XY$, $XZ$ and $ZY$ on the same side. The midpoints of the arcs are $M1$, $M2$ and $M3$ respectively. A circle ...
0
votes
1answer
477 views

Find the shortest distance between $9x^2+9y^2-30y+16=0$ and $y^2=x^3$

Find the shortest distance between $9x^2+9y^2-30y+16=0$ and $y^2=x^3$. I know the shortest distance exists between the curves on the common normal line. Is there any other shorter way to attempt?
0
votes
1answer
104 views

Questions related to vectors and linear algebra

1) Given vectors $u = (1, 1, -2)$ and $v = (0, 1, 1)$, find the value of $t$ such that magnitude of $u + t(v)$ has the smallest value I have no idea how to begin. 2) Given vectors $u = (1, 1, -2)$, ...
0
votes
1answer
65 views

Euclidean Conjugation group

Having a tad bit trying to prove this question, Show that the set of reflections is a complete conjugacy class in the euclidean group E. Also, do the same for the set of half-turns and inversions. ...
0
votes
1answer
121 views

there are two docks

There are two docks, dock A and Dock B, on a large lake. The distance between the two docks is 72.5 km. Dock B is directly east of dock A. One day, a steam boat leaves from dock A at noon, and heads ...
1
vote
1answer
75 views

Locus perpendicular to a plane in $\mathcal{R}^4$

I have solved an exercise but I'm not sure to have solved it perfectly. Could you check it? It's very important for me.. In $\mathcal{R}^4$ I have a plane $\pi$ and a point P. I have to find the ...
1
vote
2answers
237 views

Euclidean geometry exercise

I would like some help to solve this: Consider a triangle $\triangle ABC$ with $\angle A$ a right angle and $BC=20$. Divide $BC$ into four congruent segments, that is, take the points ...
1
vote
1answer
604 views

Pythagorean theorem

We can make a square into four equal squares. Fine, if we want to make into five.. Then there is a problem. Please discuss, How to make five squares from a single square by using a Pythagorean ...
1
vote
3answers
69 views

Represent lengths rectangle using given terms

In a rectangle, $GHIJ$, where $E$ is on $GH$ and $F$ is on $JI$ in such a way that $GEIF$ form a rhombus. Determine the following: $1)$ $x=FI$ in terms of $a=GH$ and $b=HI$ and $2)$calculate $y=EF$ in ...
0
votes
1answer
358 views

Prove that intersection of diagonals in trapezium divide parallel segment to equal segments

I've got exercise to do as en exercise to my school leaving exam and I have no idea how to prove it: Diagonals of trapezium intersect in point $S$. Through point $S$ the segment was given that ...
2
votes
2answers
557 views

Euclidean Geometry Intersection of Circles

Two circles intersect in the Cartesian Coordinate system at points $A$ and $B$. Point $A$ lies on the line $y=3$. Point $B$ lies on the line $y=12$. These two circles are also tangent to the x-axis at ...
2
votes
1answer
42 views

Relationship Between Three Incircles

Suppose we have a right triangle $ABC$ with hypotenuse $AB$. Further, suppose the altitude from $C$ hits hypotenuse $AB$ at point $D$. If the inradius of $ACD$ is $r_1$ and the inradius of $BCD$ is ...
1
vote
3answers
286 views

Systems of equations finding right triangles

I need help setting up the equation for the question, "Find all right triangles for which the perimeter is $24$ units and the area is $24$ square units." I know that the area is $A = \frac12 b h$ ...
2
votes
1answer
85 views

Prove that $\vec{EA}+\vec{EB}+\vec{EC}+\vec{ED}=2\vec{EO}$

Let there be a circle $(O,R)$ and $AB,CD$ two perpendicular chords of that circle that intersect on point $E$. Prove that $\vec{EA}+\vec{EB}+\vec{EC}+\vec{ED}=2\vec{EO}$
2
votes
3answers
246 views

Algebra in trigonometry, algebraic proof?

The picture says it all. "Vis at" means "show that". My first thought was that h is 2x, which is not correct. Maybe the formulas for area size is useful? EDIT: (To make the question less dependent ...
4
votes
3answers
88 views

Acute triangle: circles with diameters of two sides meet on the third

Let an acute triangle ABC be given. Prove that the circles whose diameters are AB and AC have a point of intersection on BC. How do I go about this problem? Can You Please Give Me a Hint?
0
votes
2answers
1k views

Centroid,orthocentre,incentre,circumcentre problem

How to prove that In an isoceles triangle circumcentre,centroid,orthocentre,incentre are collinear.
0
votes
2answers
422 views

Math problem- geometry- arbitrary points

an arbitrary point P is chosen on side BC of triangle ABC and perpendiculars PU and PV are drawn from P to other two sides of the triangle. (It may be that U or V lies on an extension of AB or AC and ...
4
votes
2answers
208 views

Analytic Geometry | Two Planes and a Angle | Two Solutions

this is me again, I have another problem which I haven't been able to solve, the legend goes like this: Find the equation of the plane that contains the points $P_1(1,0,-1)$, $P_2(2,0,2)$ and forms a ...