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.