Question

9. In the following figure, the line ABCD is
perpendicular to PQ; where P and are the
centres of the circles. Show that:
(i) AB = CD, (ii) AC = BD.
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Answer 1

Answer:

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Step-by-step explanation:

In circle with centre P,

OB=OC - perpendicular drawn from centre bisects the chord( or PCBC) - (1)

In circle with centre Q,

AO=DO- PCBC

Subtracting OC on both sides, sice OB=OC-from 1

AO-OB=DO-OB

AB=CD- (2)

Adding BC on both sides,

AB+BC=CD+BC

Therefore, AC= BD.

hence proved.

Answer 2

Step-by-step explanation:

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