Draw a circle of radius 5cm. Take a point P on the circle. Draw the tangent of the circle at point P without using the centre of the circle.

Step1: Take distance 5 cm in compass and draw a circle and take a point P on circle

Step2: Draw a chord PQ and subtend an angle ∠PRQ on the major arc of the circle

Using the alternate segment theorem, we will draw an ∠QPT congruent to ∠PRQ so that the line passing through PT will be tangent to circle at point P
Step3: Take any distance in compass keep the needle on point R and mark an arc intersecting PR and QR at J and K respectively

Step4: Keeping the distance in the compass same as that in step3 keep the needle on P and mark an arc intersecting PQ at S

Step5: Measure the distance of arc JK in compass, keep the needle on point S and mark an arc intersecting the arc drawn in step4 at point T. Draw line passing through point P and T and it is the tangent.