Mathematics
In the figure (i) given below, OD is perpendicular to the chord AB of a circle whose center is O. If BC is a diameter, show that CA = 2OD.
Circles
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Answer
Since, the perpendicular to a chord from the centre of the circle bisects the chord,
∴ AD = DB
We can say that D is mid-point of AB.
Since, BC is diameter and O is center so, OB = OC = radius.
We can say that O is mid-point of BC.
In △ABC,
Since, D is mid-point of AB and O is mid-point of BC
By mid-point theorem,
⇒ OD || AC and OD =
⇒ AC = 2OD.
Hence, proved that CA = 2OD.
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