Question

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

Answer 1

In the circle with center Q, QO ⊥ AD

∴ OA = OD                ...(i) ...[perpendicular drawn the center of a circle to a chord bisects it]

In circle with center P, PO ⊥ BC

∴ OB  = OC                 ....(ii)  ....[perpendicular drawn the center of a circle to a chord bisects it]

(i) - (ii) gives,

AB = CD            ...(iii)

(ii) Adding BC to both sides of equation (iii) 

 AB + BC + CD + BC

⇒ AC = BD