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Construction of Tangents to a Circle

To draw a tangent at a given point of a circle, whose centre is unknown.

A circle and a point P on its circumference.

To draw a tangent to the circle at P.

Steps of Construction
1.  Draw any chord PQ of the circle.
Take any point R other than P and Q in the major arc .
  Join PR and QR.
4. At P, describe an angle
QPT = PRQ. Then PT is the required tangent.



Draw a circle C (O,3 cm) and from a point P outside the circle draw two tangents to the circle.


Steps of Construction

1. Join OP and bisect it. Let the mid-point of OP be M.
2. With M as the centre and the radius equal to MO, draw a circle intersecting the given circle C (O,3 cm) at A and B.
3. Join AP and BP. Then AP and BP are the required tangents to the given circle.


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