# Circles - Class 9 - Mathematics

Renews every month. Cancel anytime

### Your personal doubt-solving assistant

Chatterbot AI gives you 100% accurate answers to your questions in an instant.

## 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**.