Q. 44.8( 6 Votes )

Construct tangents at the ends of the diameter of a circle of radius 3 cm. With the tangents intersect each other? Give reason for your answer.

Answer :

Steps of Construction:


1. Draw a circle with center O and radius 3cm.


2. Draw a diameter AB of this circle.



3. Extend OA such that OA=AP.


4. Extend OB such OB=BQ.



5. Draw a perpendicular bisector of OP.


6. This perpendicular bisector is the tangent at A.



7. Draw a perpendicular bisector of OQ.


8. This perpendicular bisector is the tangent at B.



No, these tangents will not intersect. They are parallel lines. Sum of internal angles is 180°. That’s why they are parallel.


CAO + DBO = 90° + 90° = 180°


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