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:
“When the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators; the instruments, not the guides, of the people.”
—Edmund Burke (1729–1797)
“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)
“No construction stiff working overtime takes more stress and straining than we did just to stay high.”
—Gus Van Sant, U.S. screenwriter and director, and Dan Yost. Bob Hughes (Matt Dillon)