From the given figure, a tangent is constructed to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm. Find the length of the tangents from point P and A.

From figure, in ∆OAP,

OA = 4 cm, OP = 6 cm AP = ? 

Tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore,  $\angle$OAP = 90^o    

Hence, ∆OAP is right angle triangle.

Substituting the given values, we get:

OA² + AP² = OP²

Substituting the given values, we get:

(4)² + (AP)² = (6)²
AP² = 36 – 16 = 20
AP = $\sqrt{20}$ 

Therefore, the length of the tangent from point P is  $\sqrt{20} cm.$

Since the circle is symmetric with respect to the tangent line, the length of the tangent from point A will also be $\sqrt{20} cm.$