1.

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 is by actual calculation.

Answer»

Solution :Steps of Consstruction :
1. Draw two concentric CIRCLES `C_(1),C_(2)` of radil 3 cm and 5 cm respectively taking 'O' as centre.
2. DREW CIRCLE `C_(3)` taking radius TM = OM and M as centre.
4. Circle `C_(3)` intersect the circle `C_(1)` at P and Q. Join TP and TQ. These are the required tangents. TP = TQ = 4.1 cm by measuring.
Mathematically Length of Tangent : Join OP. OP and TP are radius and tangent respectively at contact point P. So, `angleTPO =90^(@).` By Pythagoras THEOREM in `DeltaTPO,`
`""PT^(2)=OT^(2)-OP^(2)=5^(2)-3^(2)=25-9=16`
`implies""PT=4cm`
Difference in measurment and by mathematical calculation
`""PT=4.1cm-4cm=0.1cm`


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