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.
Answer:
Draw a circle with any radius and center ^@O^@. Draw two chords ^@PQ^@ and ^@RS^@. With center ^@P^@ and radius more than half of ^@PQ^@, draw arcs on each side of the chord ^@PQ^@. With center ^@Q^@ and same radius, draw arcs cutting the previous arcs at ^@A^@ and ^@B^@ respectively. Join ^@AB^@. With center ^@R^@ and radius more than half of ^@RS^@, draw arcs on each side of chord ^@RS^@. With center ^@S^@ and same radius, draw arcs cutting the previous arcs at ^@C^@ and ^@D^@ respectively. Join ^@CD.^@ ^@AB^@ and ^@CD^@ are the required perpendicular bisector of ^@PQ^@ and ^@RS^@ respectively. - Both perpendicular bisector ^@AB^@ and ^@CD^@ intersect each other at the center of the circle.