Question

Draw a line AB and take two points C and E on opposite sides of AB. Through C, draw \[CD\bot AB\] and through E draw \[EF\bot AB\] by using the ruler and compasses.

Answer 1

Hint: We construct the required figure by drawing the lines and point one by one.
Here, as we are not mentioned with the length and dimensions we can take the dimensions of our choice.
We draw the required figure by following the required order using the ruler and compasses.
We use the condition that the tangent to a circle is perpendicular to the radius.


Complete step by step answer:
We are asked to construct a figure by using the ruler and compass
First let us draw a line AB of any length as follows

Now, let us take two points C and E on either side of the line AB
Here, we can see that the distances of the points are not given.
Let us assume some distance for point C and point E by using the ruler then we get

We are given only a ruler and compass but not a protractor.
We know that the condition that the tangent to a circle is perpendicular to the radius.
So, let us construct the circles having the centres C and E so that AB will be tangent.
So, let us use the compass to draw two circles taking the radius as the distance between line AB and point C and E and centres as A and E then we get

Now, let us name the points both circles with centres C and E touch the line AB as D and F respectively and by joining them we get

By using the condition that the tangent to circle is perpendicular to the radius to the above figure we get \[CD\bot AB\] and \[EF\bot AB\]
Now, by removing the circles in the above figure then we get the required figure as

Therefore, we can conclude that the required figure has been constructed.

Note:
Students may do mistakes in drawing the required figure using the given instruments.
We have the figure after taking the points C and E as

We are given only a ruler and compass but not a protractor. If we have a protractor then we can directly measure the angle \[{{90}^{\circ }}\] to construct \[CD\bot AB\] and \[EF\bot AB\]
But we are not given the protractor but we are given with compass used to draw circles.
Then we use the condition that the tangent to a circle is perpendicular to the radius to construct the required figure.