Draw a circle of radius 6 cm. From a point 10 cm away from its center, construct the pair of tangents to the circle and measure their lengths.

A Pair to tangents to the given circle can be constructed as follow.
Step 1:
Takking any point 0 of the given plane as centre, draw a circle of 6 cm radius. Locat point P, 10 cm away from O. Join OP.
Step 2
Bisect OP. Let M be the mid-point of PO.
Step 3
Taking M as centre and MO as dadius, draw a circle.
Step 4
Let this circle intersect the previous circle at point Q and R.
Step 5
Join PQ and PR. PQ and PR are the required tangents. The lengths of tangents PQ and PR are 8 cm each.
Justification
The construction can be justified by proving that PQ and PR are the tangents to the circle ( whose centre is O and radius is 6 cm ). For this, join OQ and OR.
∠PQO is an angle in the semi- circle. We know that angle in a semi- circle is a right angle.
∴ ∠PQO = 90° ⇒ OQ ⊥PQ
Since OQ is the radius of the circle, PQ has to be a tangent of the circle. Similarly, PR is a tangent of the circle.