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
Draw a circle with centre at $0.$ We draw two chords $AB$ and $CD$ as shown in the figure.
$i.\ $With $A$ as centre and radius more than half of $AB,$ draw arcs on both sides of $AB.$
$ii.\ $With the same radius and $B$ as centre, draw arcs cutting the arcs of step $(i)$ at $P$ and $Q.$
$iii.\ $Join $P$ and $Q.$
$iv.\ $With $C$ as centre and radius more than half of $CD,$ draw arcs on both sides of $CD.$
$v.\ $With the same radius and $D$ as centre, draw arcs cutting the arcs of step $(iv)$ at $R$ and $S.$
$vi.\ $Join $R$ and $S.$
We draw the line segments of perpendicular bisector of $AB$ and $CD.$
We see that the perpendicular bisector of $AB$ and $CD$ meet at $0,$ the centre of the circle.
$i.\ $With $A$ as centre and radius more than half of $AB,$ draw arcs on both sides of $AB.$
$ii.\ $With the same radius and $B$ as centre, draw arcs cutting the arcs of step $(i)$ at $P$ and $Q.$
$iii.\ $Join $P$ and $Q.$
$iv.\ $With $C$ as centre and radius more than half of $CD,$ draw arcs on both sides of $CD.$
$v.\ $With the same radius and $D$ as centre, draw arcs cutting the arcs of step $(iv)$ at $R$ and $S.$
$vi.\ $Join $R$ and $S.$
We draw the line segments of perpendicular bisector of $AB$ and $CD.$
We see that the perpendicular bisector of $AB$ and $CD$ meet at $0,$ the centre of the circle.
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