Draw two concentric circles of radii 3cm and 5cm. From a point on the outer circle, construct a pair of tangents to the inner circle. Measure their lengths and verify the measurement by actual calculation.??

Steps of construction of tangents:-
Step 1
Take a point O and draw two concentric circles of radii 3 cm and 5 cm respectively.
Step 2
Locate a point P on the circumference of larger circle.
Step 3
Join OP  and bisect it . Let M be the midpoint of OP.
Step 4
Taking M as centre and MP(or MO) as radius,draw a circle intersecting smaller circle at A and B.
Step 5
Join PA and PB .Thus PA and PB are the required tangents.

Now after measuring PA and PB comes out to be 4 cm

Verification of measurement by actual calculation:-
Join OA

$$\begin{gathered} Now in ∆POA \\ Since PA is a \tan gent to the circle so OA\perp AP. \\ Thus POA is a right angled triangle \\ U\sin g pythagoras theorem \\ P{A}^2+O{A}^2=O{P}^2 \\ \Rightarrow P{A}^2=O{P}^2-O{A}^2 \\ \Rightarrow P{A}^2=(5cm{)}^2-(3 cm{)}^2 \\ \Rightarrow P{A}^2=16 c{m}^2 \\ \Rightarrow PA = 4 cm thus verified \end{gathered}$$