Question

in the adjoining figure,AB is a chord of a circle with centre O and BC is a diameter. if OD bisects AB , show that CA=2OD and CA||OD.​

Answer 1

hi dear

your answer is

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=21×AC

By cross multiplication 

AC=2×OD

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

hopes its helps you

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