Question

OD is perpendicular on chord AB of the circle with centre O.If BC is the diameter , show that AC||DO and AC =2×OD.

Answer 1

Since,
BC is the diameter,
O is the midpoint of B.C..
And,
A perpendicular from the centre bisects the chord.
Therefore,
D is the midpoint of AB.
In triangle BCA,
O is the midpoint of BC and D is the midpoint of AB.
Therefore,
DO||AC and DO=1/2AC.(Using mid point theorum).
Hence,Proved.
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