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

Now in POA Since PA is a tangent to the circle so OAAP.Thus POA is a right angled triangleUsing pythagoras theorem   PA2+OA2=OP2PA2=OP2-OA2PA2=(5cm)2-(3 cm)2PA2=16 cm2PA = 4 cm    thus verified 

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