Sol:
Given: A Circle with centre o, which ABCD is a parallelogram
To prove: ABCD is a rhombus
Ab= BC= CD= DA
Proof Since AP= AS= CD
PB= BQ---(2)
CR= QA ---(3)
RD=DS ---(4)
Adding (1) (2) (3) & (4)
Ap PB CR RD= As DS BQ QC
AN CD = AD BC
AB Ab = AD AD
2 AB = 2 AD
Ab= AD---(5)
Similarly AD= DC --(6)
DC=BC ---(7)
BC= QB --(8)
From (5) (6) & (8) we have
AB = BC = CD = AD
~ ABCD is a rhombus
Written on March 5, 2020, 4:18 p.m.