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  • Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

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Solution
 

Steps of construction
1.   Draw two concentric circles with centre O and radii 3 cm and 5 cm
2.   Taking any point P on the outer circle, Join P and O
3.   Draw a perpendicular bisector of OP let M be the midpoint of OP
4.   Taking M as the centre and OM as the radius draw a circle which cuts the inner circle at Q and R
5.   Join PQ and PR. Thus PQ and PR are required tangents 
On measuring PQ and PR we find that PQ = PR = 4 cm
Calculations
\bigtriangleup OQP, \angle OQP= 90^{\circ}
OP^{2}= OQ^{2}+PQ^{2} [using Pythagoras theorem]
\left ( 5 \right )^{2}= \left ( 3 \right )^{2}+\left ( PQ \right )^{2}
25-9= PQ^{2}
16= PQ^{2}
\sqrt{16}= PQ
4cm= PQ
Hence the length of both tangents is 4 cm.

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infoexpert27

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