Question

The figure shows two concentric circles and AD is a chord of larger circle. Prove that:AB=CD.

Answer 1

Here,
AD=AB+BC+CD, 1eq
AD=AC+BD
Ac=Ab+bc
Bd=Bc+cd
here 1eq
Ad=Ac+bd
as bc is common
AC=BD
AB+BC=BC+CD CUT BC AS COMMON
So, AB=CD PROVED.

Answer 2

Answer:

Drop OP ⊥ AD ∴ OP bisects AD (Perpendicular drawn from the centre of a circle to a chord bisects it) AP = PD ……………. (i) Now, BC is a chord for the inner circle and OP ⊥ BC ∴OP bisects BC (Perpendicular drawn from the centre of a circle to a chord bisects it)