Case I: When centre of the circle is known.
Construction 1: Draw a circle of 4 cm diameter. Take a point P on the circle. At P draw a tangent line to the circle.
Steps of Construction:
1. With centre O and radius = 2 cm, draw a circle.
2. Take any point P on sits circum ference.
3. Join O with P.
4. At, P draw PT ^ OP.
Then PT is the required tangent to the circle at the point P.
Case II: To draw tangent to a circle at a given point on it when the centre of circle is not known.
Construction 2: Draw a circle of radius 2.5 cm. Take a point P on it. Without using the centre draw a tangent to the circle at P.
Steps of Construction:
1. Draw a circle of 2.5 cm radius.
2. Take any point P cn it.
3. Through P draw any chord PR
4. Make an angle say ∠PQR in the major segment.
5. At P, draw ∠RPT = ∠PQR such that P and Q lie on opposite sides of PR.
Then TPT is the required tangent line.
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