Steps of Construction:

Step I: With O as a centre and radius equal to 6 cm, a circle is drawn.

Step II: A point P at a distance of 10 cm from the centre O is taken. OP is joined.

Step III: Perpendicular bisector OP is drawn and let it intersected at M.

Step IV: With M as a centre and OM as a radius, a circle is drawn intersecting previous circle at Q and R.

Step V: PQ and PR are joined.

Thus, PQ and PR are the tangents to the circle.

On measuring the length, tangents are equal to 8 cm.

PQ = PR = 8cm.

Justification:

OQ is joined.

∠PQO = 90° (Angle in the semi circle)

∴ OQ ⊥ PQ

Therefore, OQ is the radius of the circle then PQ has to be a tangent of the circle.

Similarly, PR is a tangent of the circle