In the adjoining figure OD is perpendicular to the chord AB of a c | Filo
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In the adjoining figure is perpendicular to the chord of a circle with centre . If is a diameter, show that and

Solution:
Perpendicular from the centre of a circle to a chord bisects the chord 

We know that

From the figure we know that is the midpoint of

We get 


We also know that is the midpoint of

We get


Consider

Using the midpoint theorem

We get and 


By cross multiplication 


Therefore, it is proved that and
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