Draw a circle with centre at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect?

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Bisector of a line segment is at right angle to the line segment. Hence steps of construction for perpendicular bisector will be the same as that of bisector of a line segment.
Steps of construction.

i. Draw a circle with centre O.

ii. Draw any two chords AB and CD such that AB is not parallel to CD.

iii. With A as centre and radius more than half of AB, draw two arcs above and below AB.

iv. With B as centre and same radius draw two arcs intersecting the previous arcs at L and M.

v. Join LM.

vi. Then LM is the perpendicular bisector of AB.

vii. Similarly, draw RS the perpendicular bisector of CD.

viii. LM and RS intersect at O, the centre of the circle.

Answered by  | 4th Jun, 2014, 03:23: PM