Tangents drawn from an external point

As performed in real lab:

Materials Required:

colored paper, pair of scissors, ruler, sketch pen, compass, pencil.


1.Draw a circle of any radius on a coloured paper and cut it. Let O be its centre.

2.Paste the cutout on a rectangular sheet of paper.[Fig 10(a)]

3.Take any point P outside the circle.

4.From P fold the paper in such a way that it just touches the circle to get a tangent

5.PA (A is the point of contact). [Fig 10(b)]. Join PA.

6.Repeat step 4 to get another tangent PB to the circle (B is the point of contact).

7.[Fig 10(c)]. Join PB.

8.Join the centre of the circle O to P, A and B. [Fig 10(d & e)]

9.Fold the paper along OP. [Fig 10(f)] What do you observe?



As performed in the simulator:

1.First draw a circle with centre O.

2.Take any point P outside the circle.

3.Click on point P to draw two tangents.

4.Click on point O to draw two perpendicular points

5.Click on triangle AOP to draw its  image.

6.Drag the  image of triangle AOP over triangle BOP.



 Students will observe that:

  •  OPA and OPB completely cover each other.
  •  Length of tangent PA = Length of tangent PB.