Circles - Class 9 - Mathematics
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Extra Questions - Circles | NCERT | Mathematics | Class 9
Draw a circle of radius $3$ cm and mark two chords $AB$ and $AC$ of the circle of lengths $4$ cm and $5$ cm, respectively, using ruler and compasses only. Then the locus of points, inside the circle, that are equidistant from $A$ and $C$ passes through the centre of the circle.
A) True
B) False
The correct option is A) True
Steps of construction:
Draw a circle with a radius of $3$ cm and mark the center as $O$.
Select a point $A$ on the circle.
With $A$ as the center and a radius of $4$ cm, draw an arc intersecting the circle at point $B$.
Using $A$ again as the center, but now with a radius of $5$ cm, draw another arc intersecting the circle at point $C$.
Connect points $AB$ and $AC$.
Construct the perpendicular bisector of segment $AC$, which we'll call line $I$. Let it intersect $AC$ at midpoint $M$ and the circle at points $E$ and $F$.
Explanation:
The locus of points inside the circle that are equidistant from two-points $A$ and $C$ is the perpendicular bisector of segment $AC$.
Line $I$, the constructed perpendicular bisector of $AC$, acts as this locus.
Conclusion:
From the construction, it is observed that line $I$, which holds the locus of points equidistant from $A$ and $C$, passes through $O$, the center of the circle. Hence, the statement is true.