To draw Tangent to a given circle at any point on it

 1) With centre ‘O’, draw a circle of any radius, and mark a point ‘P’ on it.

2) Draw a line joining O and P.

3)  Extend this line OP to Q so that OP=PQ.

4) Take any convenient radius and O as centre draw an arc as shown below,

5)  By taking same radius and Q as centre draw another arc cutting previously drawn arc as shown

6) Draw a line through P and R. Then this line is the required Tangent.

Question

1) Construct a tangent at any point P on a circle of radius 3 cm.

2) Draw a circle of radius 4 cm and construct a tangent at any point on the circle.