Draw a circle with its two chords ^@PQ^@ and ^@RS^@ such that ^@PQ^@ is not parallel to ^@RS^@. Draw the perpendicular bisector of ^@PQ^@ and ^@RS^@. At what point do they intersect each other?
Justify the steps of construction.


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Answer:

O PQ RS B A CD

Step by Step Explanation:
  1. Draw a circle with any radius and center ^@O^@.O
  2. Draw two chords ^@PQ^@ and ^@RS^@.O PQ RS
  3. With center ^@P^@ and radius more than half of ^@PQ^@, draw arcs on each side of the chord ^@PQ^@.O PQ RS
  4. With center ^@Q^@ and same radius, draw arcs cutting the previous arcs at ^@A^@ and ^@B^@ respectively.O PQ RS B A
  5. Join ^@AB^@.O PQ RS B A
  6. With center ^@R^@ and radius more than half of ^@RS^@, draw arcs on each side of chord ^@RS^@.O PQ RS B A
  7. With center ^@S^@ and same radius, draw arcs cutting the previous arcs at ^@C^@ and ^@D^@ respectively.O PQ RS B A CD
  8. Join ^@CD.^@ ^@AB^@ and ^@CD^@ are the required perpendicular bisector of ^@PQ^@ and ^@RS^@ respectively.O PQ RS B A CD
  9. Both perpendicular bisector ^@AB^@ and ^@CD^@ intersect each other at the center of the circle.

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