Using a compass and straight edge only mark two points A and B. Draw the line #l# through them and find another point C on #l# such that AB = BC?

Answer 1

Draw a line from A extending through B using the straight edge.
Use compass with center B and radius |AB| to draw a circle.
C is the point of intersection of circle and the line (other than point A)

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Answer 2

Avery Allen

To construct point C such that AB = BC on line l using a compass and straightedge:

Using the straightedge, draw line AB through points A and B.
With the compass, set the width to the distance between points A and B.
Place the compass point at point B and draw an arc intersecting line AB.
Label the intersection point as C.
Now, AC = BC = AB, satisfying the condition AB = BC.

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