How To Draw A Pentagon In A Circle

Question 1

I'chiliad not sure if this one is Gauss', but here'southward the ane I use:

Draw a circumvolve. Permit the middle be $O$.
Ascertain a direction every bit "left" and depict a line from the center going "left" until yous hit the circle. This segment is $OA$.
Draw some other line segment, this fourth dimension going "up" (this is perfectly legal - you should know how to construct a perpendicular line to a segment). This segment is $OB$.
Notice the midpoint of $OA$, calling it $Thou$.
Draw $BM$.
Find the angle bisector of $BMO$ and describe until you hitting $OB$. Call this intersection $I$.
Draw a perpendicular line to $OB$ going "left" until you hit the circumvolve at a bespeak $C$. $BC$ is now 1 line segment of the pentagon and the rest is relatively simple (just draw circle centered around $C$ passing through $B$ to get third vertex, etc.)

Something like this:

Answer · 2017-01-18 03:59:21Z

I'chiliad not sure if this one is Gauss', but here'southward the ane I use:

Draw a circumvolve. Permit the middle be $O$.
Ascertain a direction every bit "left" and depict a line from the center going "left" until yous hit the circle. This segment is $OA$.
Draw some other line segment, this fourth dimension going "up" (this is perfectly legal - you should know how to construct a perpendicular line to a segment). This segment is $OB$.
Notice the midpoint of $OA$, calling it $Thou$.
Draw $BM$.
Find the angle bisector of $BMO$ and describe until you hitting $OB$. Call this intersection $I$.
Draw a perpendicular line to $OB$ going "left" until you hit the circumvolve at a bespeak $C$. $BC$ is now 1 line segment of the pentagon and the rest is relatively simple (just draw circle centered around $C$ passing through $B$ to get third vertex, etc.)

Something like this:

Question 2

I only know two constructions. The outset I learned in high school and involves straightedge and compass: enter image description here

The other I learned in college equally I studied compass-simply (Mohr-Mascheroni) constructions. Ironically the compass-only construction is one of the simplest constructions Ive seen, just requiring 10 circles, the line-segments at the terminate are cosmetic.

enter image description here

Answer · 2020-08-19 04:36:18Z

I only know two constructions. The outset I learned in high school and involves straightedge and compass: enter image description here

The other I learned in college equally I studied compass-simply (Mohr-Mascheroni) constructions. Ironically the compass-only construction is one of the simplest constructions Ive seen, just requiring 10 circles, the line-segments at the terminate are cosmetic.

enter image description here