1. ## misli

- given the angle $C_1C_2C_3$

- straightedge and compass , straight line $C_2C_3$ , is divided into two equal parts, point $C_4$
- straightedge and compass , straight line $C_2C_4$ , is divided into two equal parts, point $C_5$
- compass $C_2C_5$ , from the point $C_2$, point $C_6$
- straightedge and compass, angle bisection $C_1C_2C_3$ , point $C_7$
- straightedge , straight line $C_2C_7$

- compass $C_2C_3$ , from the point $C_2$ , arc $C_3C_1$
- compass $C_5C_6$ , from the point $C_3$ , point $D_1$
- compass $C_5C_6$ , from the point $D_1$ , point $D_2$
- compass $C_5C_6$ , from the point $D_2$ , point $D_3$
- straightedge , straight line $C_3D_3$
- straightedge and compass, angle bisection $C_3D_3$ , point $D_4$
- straightedge , straight line $C_2D_4$ , point $D_5$

YOU TRY TO KEEP ... Figure down

2. ## Re: misli

- straightedge and compass , perpendicular to the line $a_1$ straight line $C_2C_7$
- compass $C_3D_5$ , in point $C_2$ , points $E_1 and E_2$
- straightedge and compass , perpendicular to the line $a_2$ line $a_1$ , point $E_3$
- straightedge and compass , perpendicular to the line $a_3$ line $a_1$ , point $E_3$
- straighedge , straight line $E_3E_4$ , point $E_5$
- straightedge and compass , perpendicular to the line $a_4$ straight line $C_5C_6$ , point $E_6$
- straightedge and compass , perpendicular to the line $a_5$ straight line $C_5C_6$ , point $E_7$

YOU TRY TO KEEP ... Figure down

3. ## Re: misli

- straightedge and compass , perpendicular $b_1$ straight line $C_2D_5$
- straightedge and compass , perpendicular $b_2$ on the $b_1$ from point $D_3$ , straight line $D_6D_3$
- straightedge and compass , perpendicular $b_3$ on the $b_1$ from point $D_2$ , straight line $D_7D_2$

YOU TRY TO KEEP ... Figure down
$F_1$ is located on the arc $C_3C_1$, $C_3F_1=C_1F_1$

4. ## Re: misli

- straightedge , straight line $C_2F_1$ , $C_2F_1=C_2C_3$
- compass $C_2E_5$ , from point $C_2$ , point $F_3$
- straightedge and compass , straight line the normal to $C_2F_3$
- compass $D_6D_3$ , from point $C_2$ , point $F_4$
- straightedge ,straight line extension $C_2F_4$
- compass $D_7D_2$ , from point $C_2$ , point $F_5$
- straightedge and compass , normal from point $F_5$ na duž $C_2F_1$ , point $F_6$

Solution - in the picture below

5. ## Re: misli

Do you have a question? What is supposed to be true of these? What was your point in posting them?

6. ## Re: misli

- compass $C_2F_6$ , from point $E_6$ , point $A_{12}$
- compass $C_2F_6$ , from point $E_7$, point $A_{13}$
- straightedge , semi-line $C_2A_{11}$
- straightedge , semi-line $C_2A_{12}$

trisection is complete, any error !!!

this is true for angles $180^o<\alpha<0^o$, larger angles of first division of the $180^o$

are you ready for the process of construction of the regular polygon

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HallsofIvy -question
1.if my trisection possible ?
2.from the picture below, if you can figure out which actions the ball (sphere) applied in the plane ?
arc $A_7A_8=A_9A_{11}=A_{11}A_{12}=A_{12}A_{10}=\frac{A _9A_{10}}{3}$

7. ## Re: misli

valid for the odd $a={3,5,7,9,11,...}$

Proper ninth angle

- straight line $A_1A_2$
- straightedge and compass , $\frac{A_1A_2}{10}$ , point $A_4$ , $a+1$ , $a=9. followed by .9+1=10$
- straightedge and compass , $A_1A_3$ normal $A_1A_2$ , angle $C_3C_1C_2=90^o$
- compass $A_1A_4$ , from point $A_5$
- straightedge , straight line $A_4A_5$
- straightedge and compass , bisection arc $A_2A_3$ , point $A_6$

YOU TRY TO KEEP ... Figure down