Conic Section (CONIC'S)

 

Composed by:  R.Satheesh, M.E., Asst Prof., email: rsatheeshemail@gmail.com.

Hexagon given one side

HEXAGON GIVEN ONE SIDE

    We start with a line segment AF. This will become one side of the hexagon. Because we are constructing a regular hexagon, the other five sides will have this length also. 

1. Set the compass point on A, and set its width to F. The compass must remain at this width for the remainder of the construction. 

2. From points A and F, draw two arcs so that they intersect. Mark this as point O.  This is the center of the hexagon's circumcircle.

3. Move the compass to O and draw a circle. This is the hexagon's circumcircle, the circle that passes through all six vertices    

4. Move the compass on to A and draw an arc across the circle. This is the next vertex of the hexagon.   

5. Move the compass to this arc and draw an arc across the circle to create the next vertex.  

6. Continue in this way until you have all six vertices. (Four new ones plus the points A and F you started with.)    

7. Draw a line between each successive pairs of vertices.     

8. These lines form a regular hexagon where each side is equal in length to AF is  done.

Composed by:  R.Satheesh, M.E., Asst Prof., email: rsatheeshemail@gmail.com.

Pentagon inscribed in a circle

Pentagon inscribed in a circle

We start with the given circle, center O.

Note:  If you are not given the center, you can find it using the method shown in Finding the center of a circle with compass and straight edge.        

1. Draw a diameter of the circle through the center point and mark its endpoints C and M. It does not have to be vertical.      

 2. Construct a perpendicular to CM at the  point O.  

   

3. Mark the point S where it crosses the circle.  

4. Find the midpoint L of the segment SO by constructing its perpendicular bisector.

         

5. Set the compass on L, adjust its width to S or O, and draw a circle.  

6. Draw a line from M, through L so it crosses the small circle in two places. Label them N and P. 

7. Set the compass on M and adjust its width to P.     

8. Draw a broad arc that crosses the given circle in two places. Label them A and E.  

9. Set the compass on M and adjust its width to N.       

10. Draw a broad arc that crosses the given circle in two places. Label them B and D.       

11. Draw a line from A to B, then B to C etc, until you have drawn all five sides of the pentagon.   

Now the ABCDE is a regular pentagon by inscribed in the given circle is  done.

 

Composed by:  R.Satheesh, M.E., Asst Prof., email: rsatheeshemail@gmail.com.

Tangents to a circle from a point

We start with a given circle with center ‘O’ and a point ‘P’ outside the circle.          

  1.     Draw a straight line between the center ‘O’ of the given circle and the given point ‘P’. 

  2.  Find the midpoint of this line by constructing the line's perpendicular bisector.

  3.    Place the compass on the midpoint just constructed, and set it's width to the center ‘O’ of the circle. 

  4.  Without changing the width, draw an arc across the circle in the two possible places. These are the contact points ‘J’, ‘K’ for the tangents.   

  5.  Draw the two tangent lines from ‘P’ through ‘J’ and ‘K’.  

  6.  Done. The two lines just drawn are tangential to the given circle and pass through ‘P’.

      

  

Composed by:  R.Satheesh, M.E., Asst Prof., email: rsatheeshemail@gmail.com.

HOW TO DRAW A CIRCLE  PASSING

 THROUGH THREE POINTS?

Composed by:  R.Satheesh, M.E., Asst Prof., email: rsatheeshemail@gmail.com.

DIVIDE A LINE IN TO ‘n’ EQUAL PARTS

 DIVIDE A LINE IN TO ‘n’ EQUAL PARTS

Start with a line segment AB that we will divide up into 5(in this case) equal parts.    

            

Step 1  

From  point A, draw a line segment at an angle to the given line, and about the same length. The exact length is not important. 

Step 2  

Set the compass on A, and set its width to a bit less than one fifth of the length of the new line.    

   

Step 3 

Step the compass along the line, marking off 5 arcs. Label the last one C.     

Step 4  

With the compass width set to CB, draw an arc from A just below it.           

 

Step 5  

With the compass width set to AC, draw an arc from B crossing the one drawn in step 4. This intersection is point D.  

 

Step 6 

Draw a line from D to B

 

Step 7 

Using the same compass width as used to step along AC, step the compass from D along DB making 4 new arcs across the line.

Step 8  

Draw lines between the corresponding points along AC and DB.   

Step 9 

The lines divide the given line segment AB in to 5 congruent parts is done.

           

     

           

Composed by:  R.Satheesh, M.E., Asst Prof., email: rsatheeshemail@gmail.com.