I am stuck on this construction:
"Show how to construct a circle to pass through two given points and to cut a given circle so that the common chord is of given length".
Any clues?
2026-03-28 01:47:38.1774662458
Circle construction
329 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GEOMETRY
- Point in, on or out of a circle
- Find all the triangles $ABC$ for which the perpendicular line to AB halves a line segment
- How to see line bundle on $\mathbb P^1$ intuitively?
- An underdetermined system derived for rotated coordinate system
- Asymptotes of hyperbola
- Finding the range of product of two distances.
- Constrain coordinates of a point into a circle
- Position of point with respect to hyperbola
- Length of Shadow from a lamp?
- Show that the asymptotes of an hyperbola are its tangents at infinity points
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 GEOMETRIC-CONSTRUCTION
- Construction of a graph from cycle $C_6$ and $C_7$ with specific properties (of specific eccentricities)
- Sequence of folds for finding intersection of two circles, given centers/radii
- Construct a triangle given a height, his base and the opposite angle
- Given the angles and diagonals of a quadrilateral, construct the quadrilateral using only a straightedge, a pencil, and a compass
- Proof of construction of inscribed regular hexagon
- Geometrically construct sides on cube
- When are we supposed to use 'constructions' in mathematical geometery proofs?
- Ruler and compass construction field extension
- What is this "easy application of the Pythagorean theorem"?
- Make a 60° angle on line $l$
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?
OK..I think I have the answer...phew..
Let us call the given points A,B and the given chord length = CD with the centre of the given circle O. If it helps in understanding in my answer I have drawn the given circle to the left and placed A, B to the right of it around the 2 o'clock position.
Join AB..construct perpendicular bisector of AB (XY). Centre of desired circle therefore lies on XY.
Draw any circle through A, B, with centre on XY to cut given circle at C', D' . Produce D'C' to meet BA produced at P.
Construct tangent to given circle PT.
Construct square with side equal to PT. Reduce constructed square to a rectangle with sides equal to PD, CD (CD is given so is known therefore PD can be constructed)
With centre P cut given circle with arc = PD at point D. Join PD. PD cuts given circle again at C giving us the desired common chord CD. Bisect CD to intersect XY giving us centre of desired circle..