REFERENCE:
Let’s say that we are given a circle with centre O and a point P outside it, and we have to construct two tangents from the point P to the circle without the help of a ruler. Follow the steps of construction as below:
1.Join OP and bisect it. To bisect OP, take a compass, and open it slightly more than half of the length of the line segment.
2.From point P, mark a minimal arc above and below the line segment. Repeat the similar step from point O keeping the opening of the compass as same as it was from point P. Two points will be created where the two arcs, produced from point O and point P, meet.
3.Join these two points with a line segment using a scale. This line segment bisects the OP. Let’s consider H as the mid-point of PO.
4.Taking the point H as a centre and HO as a radius, draw a circle. Let it intersect the given circle at the points, T and T’.
5.Join PT and PT’. Then PT and PT’ are the required two tangents.
and after following the above steps measure the tangents PT and PQ using scale.