10. CBQ - Perpendicular bisectors of chords of the circle

Question:

4 m.

In a park, a circular flower bed has a radius of 5\(m\). A straight walking path \(AB\) cuts across the circle such that it is \(4 \ m\) away from the centre.

(i) If a perpendicular is drawn from the centre to the chord \(AB\), explain what happens to the two parts of the chord on either side of the perpendicular.

The perpendicular line passes through the end points of the chord.
The perpendicular line bisects the chord.
The perpendicular line divides the chord into two unequal parts.
The perpendicular line bisects the radius.

(ii) Find the length of the path inside the circular flower bed.

(iii) If another path \(CD\) is only \(3m\) from the centre, compare its length with \(AB\).

\(CD\) is the longest chord.
\(AB\) is perpendicular to \(CD\).
Both are same
\(AB\) is the longest chord.

(iv) Explain why the chord becomes longer when it is closer to the centre.

Because, as the chord moves nearer to the centre, it becomes longer because it covers more of the circle.
Because, as the chord moves nearer to the centre, it stays the same length.
Because, as the chord moves nearer to the centre, it moves outside the circle.
Because, as the chord moves nearer to the centre, it becomes shorter.

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