Question

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

Answer 1

In the circle with centre Q, QO ⊥ AD 
∴ OA= OD        …………… (1)
(Perpendicular drawn from the centre of a circle to a chord bisects it)
In the circle with centre P, PO ⊥ BC
∴ OB=OC          ……………..(2)
(Perpendicular drawn from the centre of a circle to a chord bisects it)
(i)
(1) – (2) Gives,
AB = CD ……………(3)

(ii) Adding BC to both sides of equation (3)
AB+BC = CD+BC
⇒ AC = BD