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


Answer:

O PQ RS B A CD

Step by Step Explanation:
  1. Draw a circle with any radius and center OO.O
  2. Draw two chords PQPQ and RSRS.O PQ RS
  3. With center PP and radius more than half of PQPQ, draw arcs on each side of the chord PQPQ.O PQ RS
  4. With center QQ and same radius, draw arcs cutting the previous arcs at AA and BB respectively.O PQ RS B A
  5. Join ABAB.O PQ RS B A
  6. With center RR and radius more than half of RSRS, draw arcs on each side of chord RSRS.O PQ RS B A
  7. With center SS and same radius, draw arcs cutting the previous arcs at CC and DD respectively.O PQ RS B A CD
  8. Join CD.CD. ABAB and CDCD are the required perpendicular bisector of PQPQ and RSRS respectively.O PQ RS B A CD
  9. Both perpendicular bisector ABAB and CDCD intersect each other at the center of the circle.

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