How can one show that in every polygon circumscribed about a circle, there exist three sides that can form a triangle?
(This was posted by another user and then deleted while I was typing my answer.)
2026-03-26 07:33:27.1774510407
In every polygon circumscribed about a circle, there exist three sides that can form a triangle.
173 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in CIRCLES
- Point in, on or out of a circle
- Constrain coordinates of a point into a circle
- Circle inside kite inside larger circle
- How to find 2 points in line?
- Locus of a particular geometric situation
- Properties of a eclipse on a rotated plane to see a perfect circle from the original plane view?
- Complex numbers - prove |BD| + |CD| = |AD|
- Number of line segments to approximate a circle
- Right Angles in Circles
- Simpler Derivation of $\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}$,
Related Questions in POLYGONS
- Can the relocation of one control point of a NURBS curve be compensated by an adjustment of some weights?
- Need a hint regarding this question...
- How do I detect if a circle overlaps with a polygon or not?
- A peculiar Diophantine equation
- Looking for Regular Polygons with a Side to Diagonal ratio Equaling a Metallic Mean
- Calculating the value of $\pi$
- Bounding Numbers for $N>2$
- Generalizing Odom's construction of the golden ratio
- Integrating difficult function over a polygon
- Existence and uniqueness of a Riemann-Hilbert problem involving a polygon
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Look at the very longest side and the two sides adjacent to it.
Say the longest side has vertices $B$ and $C$ and touches the circle at $Y$. One of the adjacent sides shares vertex $B$ and touches the circle at $X$. The other shares $C$ and touches at $Z$.
Notice that the distances $BY$ and $BX$ are equal, and the distances $CX$ and $CZ$ are equal.
So a segment of length more than $BY$ and one of length more than $CZ$ have a sum of lengths more than $BY+YC$, thus satisfying the triangle inequality.