Q4 of 805 Page 10

Construct a tangent to a circle of radius 4cm from a point which is at a distance of 6cm from its centre.

Thinking process:


I. Firstly taking the perpendicular bisector of the distance from the centre to the external point. After that taking one half of bisector as radius and draw a circle.


II. Drawing circle intersect the given circle at two points. Now, meet these intersecting points to an external point and get the required tangents.


Given, a point M is at a distance of 6 cm from the centre of a circle of radius 4 cm.


Steps of construction


1. Draw a circle of radius 4 cm. Let centre of this circle is O.



2. Take a point M at 6cm away from the radius.



3. Join OM and bisect it. Now, with M and O as centres and with radius more than half of draw two arcs on the either sides of the line OM. Let the arc meet at A and B,just that, M1 be mid-point of OM.



4. Taking M1 as centre and M1O as radius draw a circle to intersect circle with radius 4 and centre O at two points P and Q.



5. Join PM and QM. PM and QM are the required tangents from M to circle with centre O and radius 4.



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