MathDB

points construction, intersecting chords related

Source: Germany 1996 p5

February 22, 2020

constructiongeometric constructiongeometry

Problem Statement

Given two non-intersecting chords

AB

and

CD

of a circle

k

and a length

a <CD

. Determine a point

X

k

with the following property: If lines

XA

and

XB

intersect

CD

at points

P

and

Q

respectively, then

PQ = a

. Show how to construct all such points

X

and prove that the obtained points indeed have the desired property.