Step-by-step explanation:

since AB and AC are two both chords then we can say AB = AC..........eq(1)

now

OD is perpendicular to AB

and bisect AB

so

OD=1/2AB

or

2OD = AB

now

AB = AC(from 1)

hence

AC= 2OD or CA=2OD

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Answer:

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

We know that OB⊥AB

From the figure we know that D is the midpoint of AB

We get

AD=BD

We also know that O is the midpoint of BC

We get

OC=OB

Consider △ABC

Using the midpoint theorem

We get OB∥AC and

OD=

2

1

×AC

By cross multiplication

AC=2×OD

Therefore, it is proved that AC∥DO and AC=2×OD

Step-by-step explanation:

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