Question

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

Answer 1

Answer:

ANSWER

(i) AB=CD

(ii) AC=BD

(i) Consider triangle PBC

BC is chord of small circle and P is center

and PO is perpendicular to BC (Given)

BO=CO...(1) (Perpendicular from center to ac chord divides the chord equally)

Consider triangle QAD

Q is center of big circle

AD is chord and QO⊥AD (Given)

AO=OD (perpendicular from center to a chor divides the chord equally)

(AB+BD)=(OC+CD)

AB+BO=BO+CD (From (1) BO=CO)

AB=CD

(ii) We know

AB=CD (from part (i))

AB+BC=CD+BC (adding BC on both sides)

AC=BD