TBQ - Demonstrate the following — task. Mathematics CBSE, Class 9 New.

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Can you explain why does the perpendicular from the centre of a circle to a chord of the circle bisect the chord?

Proof:

Consider a circle with centre \(O\) and a chord \(LM\).

Let \(ON\) be drawn perpendicular from the centre of a circle to the chord \(LM\).

Join the points \(OL\) and \(OM\).

Consider the \(\Delta OLN\) and \(\Delta OMN\).

Here, \(OL\) \(=\) [].

And, the side \(ON\) is to the triangle \(ONL\) and \(ONM\).

Also, \(ON \perp LM\) [].

So, \(\angle ONL = \angle ONM =\) \(^{\circ}\).

Therefore, \(\Delta OLN\) \(≅\) \(\Delta OMN\) []

This implies, \(NL =\) .

Therefore, perpendicular from the centre of a circle to a chord of the circle bisects the chord.

Hence, proved.

Did you find an error?

5. TBQ - Demonstrate the following