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Aim:
\[\text{Two parallel straights of V = 20m apart are to connected by a reverse curve}\ \hspace{15cm}\\ \text{consisting of arcs of same radius. The distance between the}\ \hspace{12cm}\\ \text{end points of the curve is L=200m}\ \hspace{10cm}\]
\[i.\ \text{To draw two parallel straights of 20m apart.}\ \hspace{15cm}\]
\[ii.\ \text{To draw the reverse curve joining to points on the parallel straights which}.\ \hspace{15cm}\\ \text{are 200m distance from one another.}\ \hspace{10cm}\]
\[iii.\ \text{To find the approximate value of the common radius of the reverse curve}\ \hspace{15cm}\]
\[iv.\ \text{Find the length of the whole reverse curve.}\ \hspace{15cm}\]
Procedure:
\[\color{green}{Step\ 1:}\ \text{Open Geogebra classic 5 (by double clicking on the icon)}\ \hspace{18cm}\]
\[\color{green}{Step\ 2:}\ \text{To draw the straight line by using input bar to type}\ l_1\ :y=0\ \hspace{10cm}\]
\[\color{green}{Step\ 3:}\ \text{To draw a another straight line by using input bar to type}\ l_2\ :y=20\ \hspace{10cm}\]
\[\color{green}{Step\ 4:}\ \text{To mark a point on}\ l_2,\ \hspace{20cm}\\ \text{by using the input bar type A =(l_2) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 5:}\ \text{To mark a point on}\ l_1,\ \hspace{20cm}\\ \text{by using the input bar type B =(l_1) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 6:}\ \text{To join the points A and B}\ \hspace{21cm}\\ \text{by using the input bar type L=Segment(A, B) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 7:}\ \text{To fix the point A, move the point B using the move tool}\ \hspace{18cm}\\ \text{and fix a position for B so that L = 200m}\ \hspace{14cm}\]
\[\color{green}{Step\ 8:}\ \text{To mark the midpoint C of the line segment L = AB}\ \hspace{18cm}\\ \text{by using the input command C = Midpoint(L)}\ \hspace{14cm}\]
\[\color{green}{Step\ 9:}\ \text{To draw the perpendicular bisector line of the line segment AC,}\ \hspace{18cm}\\ \text{by using the input command b1:PerpendicularBisector(A,C)}\ \hspace{14cm}\]
\[\color{green}{Step\ 10:}\ \text{To mark the point F on b1}\ \hspace{20cm}\\ \text{by using the input bar to type F=Point(b1) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 11:}\ \text{To draw the line segments AF}\ \hspace{21cm}\\ \text{by using the input commands AF=Segment(A, F) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 12:}\ \text{To draw the line segments CF}\ \hspace{21cm}\\ \text{by using the input commands CF=Segment(C, F) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 13:}\ \text{To draw the circular curve}\ \hspace{21cm}\\ \text{by using the input bar to type C1=Circular Arc(F,C,A)}\ \hspace{14cm}\]
\[\color{green}{Note:}\ \text{click and drag or move the point F on b1 so that the circular}\ \hspace{18cm}\\ \text{curve is below the line}\ l_2\ and\ l_2\ \text{is a tangent of that curve at A}\ \hspace{14cm}\]
\[\color{green}{Step\ 14:}\ \text{To draw the perpendicular bisector line of the line segment BC,}\ \hspace{18cm}\\ \text{by using the input command b2:PerpendicularBisector(B,C)}\ \hspace{14cm}\]
\[\color{green}{Step\ 15:}\ \text{To mark the point G on b2}\ \hspace{20cm}\\ \text{by using the input bar to type G=Point(b2) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 16:}\ \text{To draw the line segment BG}\ \hspace{21cm}\\ \text{by using the input bar to type BG=Segment(B, G) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 17:}\ \text{To draw the line segment CG}\ \hspace{21cm}\\ \text{by using the input bar to type CG=Segment(C, G) and press the Enter key}\ \hspace{14cm}\]
\[\color{green}{Step\ 18:}\ \text{To draw the circular curve}\ \hspace{21cm}\\ \text{by using the input bar to type C2=Circular Arc(G,C,B)}\ \hspace{14cm}\]
\[\color{green}{Note:}\ \text{click and drag or move the point G on b2 so that the circular}\ \hspace{18cm}\\ \text{curve is below the line}\ l_1\ and\ l_1\ \text{is a tangent of that curve at B}\ \hspace{14cm}\]
\[\color{green}{Step\ 19:}\ \text{To draw the circular c1}\ \hspace{21cm}\\ \text{by using the input bar to type C1=Circle (F,A,F)}\ \hspace{14cm}\]
\[\color{green}{Step\ 20:}\ \text{To draw the circular c2}\ \hspace{21cm}\\ \text{by using the input bar to type C2=Circle (G,B,G)}\ \hspace{14cm}\]
\[\color{green}{Step\ 21:}\ \text{To verify that the circular curves C1 and C2 are parts of the circles}\ \hspace{16cm}\\ \text{c1 and c2 respectively}\ \hspace{18cm}\]
\[\color{green}{Step\ 22:}\ \text{To find the length of the reverse curve from A to B}\ \hspace{16cm}\\ \text{by using the input command I =C1+C2}\ \hspace{18cm}\]
\[\color{green}{Step\ 23:}\ \text{The radius of the reverse curves is R=AF which is equal to CF,}\ \hspace{16cm}\\ \text{BG, and CG which are found in the algebra view.}\ \hspace{18cm}\]
\[\color{green}{Step\ 24:}\ \text{To create an input box for V, the distance between the}\ \hspace{16cm}\\ \text{parallel straights link with}\ I_2\ :\ y\ =\ 20\ \hspace{18cm}\]
Output:
Output for radius of curvature and length of the curve.
| Description | Formula / Value |
| Distance between parallels (V) | V = 20 |
| Distance between endpoint of the Inverse Curve (L) | L = 200 |
| Equation of the Circle c1 | |
| centre of the Circle c1 | F=(0,- 480.01) |
| Radius of the Circle c1 | AF = 500.01 |
| Equation of the Circle c2 | |
| centre of the Circle c2 | G=(199.04,500.37) |
| Radius of the Circle c2 | BG=500.37 |
| Radius of the reverse Curve (R) | 500 |
| Length of the reverse Curve (I) | I = 200.34 |
Output for variation in distance between the parallel straights (V).
| Distance Between Parallel Straights (V) | Radius of the reverse Curve (R) | Length of the reverse Curve (I) |
Output for variation in distance between the Endpoints of the Inverse Curve.
| Distance Between the Endpoints of the reverse curve (L) | Radius of the reverse Curve (R) | Length of the reverse Curve (I) |
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