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InterviewSolution
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Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation. |
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Answer» SOLUTION :Given, two concentric circles of radill 4 cm and 6 cm with common centre O. We have to draw two tangents to inner circle from a point of outer circle. Steps of Construction : 1. Draw two concentric circles with centre a O and radii 4 cm and 6 cm. 2. Take any point P on outer circle. Join OP. 3. Now, bisect OP. LET M' be the mid-point of OP. 3. Now, bisect OP. Let M' be the mid-point of OP. Taking M' as centre and OM' as radius draw a circle (dotted) which cuts the inner circle at M and P'. 4. Join PM and PP'. Thus, PM and PP' are required tangents. 5. On measuting PM and PP', we get PM = PP' = 4.47 cm. Calculation : In right `DeltaOMP,anglePMO=90^(@)` `therefore""PM^(2)=OP^(2)-OM^(2)""("by Pythagoras theorem")` `implies""PM^(2)=(6)^(2)-(4)^(2)=36-16=20` `implies""PM=sqrt20=44.47` Hence, the lenght of tangent is `4.47.` Justification : Join OM and OP' which are radius. The `angle OMP` is an angle lies in the semi-circle and therefore `angleOMP=90^(@)` `implies""OMbotOP` Since, Om is radius of the circle, so MP has to be a tangent to the circle. Similarly, PP' is also a tangent to the circle. 
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