All Questions
Tagged with triangles analytic-geometry
241
questions
2
votes
4
answers
107
views
Is there is a formula to calculate the coordinates of the orthocenter of a triangle?
I'm trying to find the coordinates of the orthocenter (the intersection point of all altitudes) of a triangle given its vertices' coordinates $A=(x_1, y_1), \ B=(x_2, y_2) , \ C=(x_3, y_3)$.
I ...
- 6,565
3
votes
6
answers
230
views
Rotating and scaling an arbitrary triangle such that the new triangle has its vertices on the sides of the original one
Given $\triangle ABC$, and a scale factor $r \lt 1 $, I want to find the necessary rotation (center and angle) such that the rotated/scaled version of the triangle has its vertices lying on the sides ...
- 24.5k
2
votes
1
answer
54
views
How to calculate the radius of an outer circle from two symmetric internally tangent circles? (Applied Wind Turbine Problem 🔧)
Motivation & Context
The below problem is related to an open-source CAD model of a locally-manufactured small wind turbine.
The generator of the turbine is made from two rotating magnetic disks ...
- 23
0
votes
3
answers
62
views
How must I find the third vertex of an equilateral / right isosceles triangle given the coordinates of 2 vertices?
This question has been asked in different ways at different points of time in the Math SE, but I'm trying to look for proof-wise simplicity here.
If the ends of hypotenuse of a right isosceles ...
- 23
6
votes
1
answer
383
views
Cutting a square and gluing it back together
I have a $1 \times 1$ square and I cut the triangle that has vertices at the center and bottom right and left corners of the square. Then I glue this triangle to the right edge of the square as shown ...
- 92
1
vote
0
answers
52
views
Can a triangle $ABC$ be translated onto another triangle $PQR$ in multiple ways?
For example, if $ABC = (0,1), (2, 3), (4, 7)$ and $PQR = (-1, -1), (1, 1), (3, 5)$, then the only way $ABC$ can be superimposed onto $PQR$ is by a translation $1$ unit left and $2$ units down. This ...
- 1,950
1
vote
1
answer
191
views
Locus of centroid, given the slopes of the sides
Find the locus of the centroid of a triangle if it is known that its orthocentre is at the origin and the slopes of the sides of the triangle are $ m_1, m_2, m_3$ respectively.
I solved this problem ...
- 739
2
votes
0
answers
63
views
Geometrical construction of the minimal area bounding square of a triangle.
Edit: The term "bounding square" in this question is shorthand for "the minimal area square that encloses the triangle".
The topic of finding the bounding square of arbitrary ...
- 1,111
5
votes
2
answers
112
views
Simple bisection geometry
Let $\triangle ABC$ have incenter $D$ and let the incircle intersect sides $BC,AB,AC$ at $E,F,G$ respectively. Extend $AB$ and $AC$ to meet the circumcircle of $\triangle ADE$ at $K$ and $I$ ...
- 109
2
votes
3
answers
101
views
Find all inscribed ellipses in a given triangle passing through two given internal points
Given a triangle, and two points inside it, I want to determine all the ellipses that are inscribed in the triangle and passing through both of the two given points.
My attempt: is outlined in my ...
- 24.5k
2
votes
2
answers
61
views
Seeking Precise Solution for Triangle Area Problem
I hope this message finds you in high spirits. I am writing to seek your expertise in solving a captivating geometry problem that I recently encountered in a competitive exam. Despite my best ...
- 522
4
votes
1
answer
161
views
Equation of a triangle. Equation of a quadrilateral. Book reference
Analytic geometry textbooks usually teach the equation of a straight line and the equations of a circle and conic sections (equation of an ellipse/hyperbola/parabola). None (except a russian one) as ...
- 728
0
votes
5
answers
440
views
Shortest distance from point to a curve and Estimation of error of an incorrect approach
Today I wrote an answer to a question in regards to the topic of shortest distance between a point and a curve, more precisely an ellipse, check here. Turns out the answer was incorrect, yet it was a ...
- 2,183
0
votes
1
answer
126
views
Calculation of Areas of Leaf-like Segments in an Equilateral Triangle [duplicate]
I hope this message finds you well. I recently came across a captivating geometry problem involving an equilateral triangle and leaf-like segments formed by intersecting arcs. I encountered this ...
- 522
0
votes
1
answer
65
views
Are there simple algebraic expressions for the intersections of a triangle's incircle and its interior angle bisectors?
We have a triangle made from three arbitrary points:
$A = (α, δ)$,
$B = (β, ε)$, and
$C = (γ, θ)$.
The side of the triangle opposite point $A$ has a length of $a$, the side opposite $B$ has length $...
- 1,861