Questions tagged [geometry]

Question 1

I'm trying to find a problem about right triangles with a minimalist statement that isn't too obvious. Here's what I've come up with : ABC is an A–right triangle, H is the orthogonal projection of A ...

Question 2

I am in the process of designing a global trajectory program for civil aircraft. Two aircraft depart from their airports, join together to create a formation, then later separate and land at their ...

Question 3

A set $C\subset \mathbb{R}^2$ is a simple curve if $\forall p \in C$ there exist $I$ an open interval, $V$ an open set in $\mathbb{R}^2$ containing $p$; and $\alpha \colon I \rightarrow \mathbb{R}^2$ ...

Question 4

Suppose you're given a triangle $\triangle ABC$ in the $xy$ plane, with known side lengths. Now you rotate and shift this triangle to some other position/orientation generating a congruent triangle $\...

Question 5

I have a right triangle $OAB$ with right angle at $O$, and let \begin{equation} OA = L, \quad OB = 1. \end{equation} Let $a$ be a point on $OA$ and $b$ a point on $OB$. From these points, ...

Question 6

In a $\triangle ABC$, with sides $a$, $b$, $c$ we are given $$a^4 + b^4 + c^4 = 2a^2c^2+2b^2c^2$$ Find possible values of $\angle C$. In this a,b,c are the sides of the triangle. Please help with ...

Question 7

This was the original problem statement: Let $ABCD$ be a quadrilateral, where $A, B,C$ and $D$ are points in anti-clockwise direction corresponding to $z_1, z_2, z_3, z_4\in\mathbb{C}$ respectively. ...

Question 8

In rectangle $ABCD$, points $P$ and $Q$ lie on sides $AD$ and $DC$ respectively, such that $AP = 2 \times DQ$. Given that $AB = 5\,\text{cm}$, $BC = 10\,\text{cm}$, and the area of quadrilateral $BPQC$...

Question 9

costruct a triangle ABC if BC=8 cm, AB+AC=15 cm, and Ha=3 cm,where Ha is the height from A to BC, using Euclid Geometry only.

Question 10

Let $ABCD$ be a square with points $F \in BC$ and $H \in CD$ such that $BF = 2FC$ and $DH = 2HC$. Construct: Line through $F$ parallel to $AB$, meeting $AD$ at $E$ Line through $H$ parallel to $BC$, ...

Question 11

We are attempting to measure roots of quintic equations in Powerpoint. This is a mathematical curiosity inspired by Dr. Zye's recent video on making flags in Powerpoint. If you are interested in the ...

Question 12

I came across this statement, that it is impossible to construct a segment of length $\sqrt[3]{2}$ (the cube root of 2) with a straightedge and compass from a unit segment. I know that one can ...

Question 13

There is a famous theorem in elementary geometry: Theorem. An isosceles triangle with a $60^\circ$ angle is equilateral. Two cases of this theorem are depicted below. I consider any (or both) of ...

Question 14

This is picture of the following problem. Here are the steps I took. Firstly, I was confused by the similar triangle statement. By doing some angle chasing I believe that ∆ABD~∆ACB. So for the rest of ...

Question 15

Let a hyperbola with semi major axis length $a$ and shortest radius $r_p$ be given. For $r\geq r_p$ find angle $\gamma$ between the tangent at distance $r_p$ and the tangent at distance $r$ from the ...

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Questions tagged [geometry]

What is the length of the height AH?

Fermat-Torricelli Weighted Point

Is every simple curve the preimage of a regular value?

A question about rotating and shifting a triangle

Similarity argument in right triangle with perpendiculars to sides

Finding possible values of $\angle C$ in $\triangle ABC$ whose sides satisfy $a^4 + b^4 + c^4 = 2a^2c^2+2b^2c^2$ [closed]

Help: Proof of Ptolemy's Inequality with Complex Numbers

Find the length of the side DQ

triangle construction by using Eyclid Geometry [closed]

Perpendiculars passing through diagonal intersection in a quadrilateral formed within a square

Solving quintic equations with PowerPoint shapes

Show that it is impossible to construct a segment of length $\sqrt[3]{2}$ (the cube root of 2) with a straightedge and compass from a unit segment? [closed]

Can an isosceles triangle with a $60^\circ$ angle be proven equilateral independently of the triangle angle sum theorem?

High School Geometry Problem involving Golden Ratio

Angle between tangents of a hyperbola

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