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Answer of the question given below Asked by bhu.joshi54 | 04 Jul, 2022, 08:18: PM Expert Answer
Given,
PQRS is a parallelogram
QR|| PS
AB||PS
∠OSP = ∠OBA ...(corresponding angles)
Also,QR|| AB
∠CRQ = ∠CBA ...(corresponding angles)
In â–³OPS and â–³OAB,
∠POS = ∠AOB ...(common angle)
∠OSP = ∠OBA ...(corresponding angles)
Hence,
â–³OPS ~ â–³OAB ...(AA test)
by CPST
PS/AB = OS/OB ...(1)
In â–³CQR and â–³CAB,
∠RCQ = ∠BCA...(common angle)
∠CRQ = ∠CBA ...(corresponding angles)
â–³CQR ~ â–³CAB...(AA test)
by CPST
QR/AB = CR/CB ...(2)
PQRS is a parallelogram
PS = QR,
from (2)
PS/AB = CR/CB ...(3)
From (1) and (3)
OS/OB = CR/CB
OB/OS = CB/CR
(OB/OS)- 1 = (CB/CR) - 1
(OB-OS)/OS = (CB-CR)/CR
From the figure,
OB - OS = BS
CB - CR = BR
Now,
BS/OS = BR/CR
So by Converse of Basic Proportionality Theorem,
SR||OC

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