Question

if a given fig, OD is perpendicular to the chord AB of a circle whose center O. if BC is a diameter. find CA/OD​

Answer 1

Step-by-step explanation:

Since, OD ⊥ AB and the perpendicular drawn from the centre to a chord bisects the chord.

∴ D is the mid-point of AB.

Also, O being the centre , is the mid – point of BC.

Thus, in ΔABC, D and O are mid-point of AB and BC respectively. Therefore, OD ∥ AC

And OD = ½ CA [∵ Segment joining the mid- points of two sides of a triangle is half of the third side]

⇒ CA = 2OD.

Hence proved.