Home > Construct with GeoGebra > Compass and Straightedge > #5 Construct a Perpendicular (Normal) > HELP
Do the givens. 

Draw a line by clicking twice in drawing pad. 
Point A
Point B
a=Segment[A,B]

Label: Use rightclick to hide/show labels on points and to rename the line m.

Make A the midpoint of line segment CB 

Draw circle with radius AB and center A by clicking on points A, B and A. 
Circle c=Circle[A, Segment[A, B] 

Draw point C by clicking on left intersection point of circle c and line m. (A is midpoint of CB.)

C=Intersect[c, m, 2]. 
Decorate: Rightclick on circle, choose "Properties" and make it thin and dotted. Click on Close. 
Get ready to draw circles with a radius bigger than 1/2 of CB. 

Draw a fourth point between A and B. (This makes it bigger than 1/2 of CB.) 
Point D
D=Point[m]

Draw 2 circles with radius CD  one with center C and other with center B. 

Draw circle with radius CD and center C by clicking on points C, D and C. 
Circle d=Circle[C, Segment[C, D] 

Draw circle with radius CD and center B by clicking on points C, D and B. 
Circle e=Circle[B, Segment[C, D] 
Decorate: Rightclick on either circle, choose "Properties". Make both circles red and dotted so you can find them. Click on Close. 
Draw an intersection points of the circles


Draw point E by clicking on top (or bottom) intersection point of red circles d and e. 
E=Intersect[c, d, 2]. 
Draw perpendiular (normal).


Draw line through E and A by clicking on points E and A. 
a=Line[D,E] 
Label: Use rightclick to rename this line n.
Decorate: Rightclick on any object, choose "Properties" and go for it! When done, click on Close.

Check construction. 

Click and drag point A (and/or point B). 
The line n should pass through A
and be perpendicular to line m. 
Save construction. Command: File > Save. 
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