In order to construct a circle of radius and two tangents from it, we make a construction using the appropriate geometrical equipment. We make use of a ruler to measure the length of the radius and an external point 8 cm from the center of the circle. Then we draw two lines to the circle from the external point such that thy touch the circle at exactly one point respectively.Complete step-by-step answer:
Radius of the circle = 3 cm
Length of the external point from the center of circle = 8 cm
The steps of construction to construct the circle and tangents to it are as follows:
First we draw a line segment of length 3 cm and name it ‘AD’, which acts as the radius of the circle.
Then with point A as the center of the circle we draw a full arc starting from point B as the other end until we make a full circle and reach point B again.
Now from point A we measure a length of 8 cm towards any direction of our choice and mark a point C there.
Now with C as the starting point we draw a line towards any edge of the circle such that it only touches the circle at one point throughout its entire course.
Now with C as the center, we repeat the same process but this time we draw the line in a different direction from the previous.
Thus we made a circle with two tangents to it from an external point.
Thus the circle with center A is obtained.
The figure obtained after we finish construction is as follows:Note
: In order to solve this type of problems the key is to know how to construct a geometrical figure with a set of given requirements, using the help of geometrical apparatus. We measure a length of straight lines using a ruler, we draw the circle using a compass to which one end is fixed at the center of circle A and the other end is placed at the point B and is freely moved in a circular direction until we reach B again. We find all these instruments in a geometrical box and each instrument has a specific use case. We do the construction in a stepwise manner.