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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