Construction
We are given points A, B, and C, and wish to construct a circle centered at A with the same radius as BC (the first green circle).
- Draw a circle centered at A and passing through B and vice versa (the red circles). They will intersect at point D and form equilateral triangle ABD.
- Extend DB past B and find the intersection of DB and the circle BC, labeled E.
- Create a Circle centered at D and passing through E (the blue circle).
- Extend DA past A and find the Intersection of the DA and the circle DE, labeled F.
- Construct a circle centered at A and passing through F (the second green circle)
- Because E is on the circle BC, BE=BC.
- Because ADB is an equilateral triangle, DA=DB.
- Because E and F are on a circle around D, DE=DF.
- Therefore, AF=BE and AF=BC.
Read more about this topic: Compass Equivalence Theorem
Famous quotes containing the word construction:
“There’s no art
To find the mind’s construction in the face:
He was a gentleman on whom I built
An absolute trust.”
—William Shakespeare (1564–1616)
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)
“Striving toward a goal puts a more pleasing construction on our advance toward death.”
—Mason Cooley (b. 1927)