Question

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?

Answer 1

We are asked to draw a circle centered at O and two chords AB and CD

We will follow the following algorithm for the construction

Steps of construction

STEP1: With centre O, draw a circle of any radius.

STEP2: Draw any two chords AB and CD, such that the two chords are not parallel.

STEP3: With centre B and taking any radius (more than half of AB), draw two arcs, one on each side of the chord AB.

STEP4: With centre A, and taking the same radius, draw two arcs, one on each side of the chord AB, cutting the previous arcs in E and F respectively.

STEP5: Draw a line segment with E and F as end-points. It passes through centre O.

STEP6: With centre C and taking any radius (more than half of CD), draw two arcs, one on each side of the chord CD.

STEP7: With centre D, and taking the same radius as in STEP 6, draw two arcs, one on each side of the chord CD, cutting the previous arcs in G and H respectively.

STEP8: Draw a line segment with G and H as end-points. This also passes through centre O. It is clear that perpendicular bisectors EF and GH intersect at point O, which is the centre of the circle.