Bisect a given line segment AB

Geometric Construction with the Compass Alone

Solution

Construct a point C such that AC = 2·AB (Problem #1). Swing an arc of radius CA with center C. This will intersect the circle of radius AB centered at A at points D and E. Draw two arcs of radii DA and EA (which are both equal to AB) and centers at, respectively, D and E. Besides A, the two arcs will intersect at another point F which is the middle of the segment AB.

Indeed, ΔACE is similar to the ΔAFE (they are both isosceles and share ∠EAF. From here, AC/AE = AE/AF. But AC/AE = 2·AB/AB = 2. Therefore, AB = AE = 2·AF.


[an error occurred while processing this directive]

|Contact| |Front page| |Contents| |Up|

Copyright © 1996-2018 Alexander Bogomolny
[an error occurred while processing this directive]
[an error occurred while processing this directive]