Q3 of 805 Page 11

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its center. Draw tangents to the circle from these two points P and Q.

Step1: Draw a circle of 2 cm radius, taking O as a center.


Step2: Take diameter PQ. Now locate two points on diameter OR and OS.


OR and OS=7cm


Step3: Bisect OR and OS


Step4: Get A and B the midpoint of OR and OS.


Step5: Now draw a circle of AO and OB radius and T and U as a center.


Step6: These two circles intersect the circle at E,F,G,H . Join RE,RF,SG,SH. They are tangents.



Justification:


For this,


Join OE, OF, OG and OH.


∠ROE=90°


OE⊥RE


Since OE=radius of circle and RE has to be a tangent.


Similarly RF, SG and SH are tangents.


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