# CBSE Class 10 Answered

**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 △OPS and △OAB,

In △OPS and △OAB,

∠POS = ∠AOB ...(common angle)

∠OSP = ∠OBA ...(corresponding angles)

Hence,

△OPS ~ △OAB ...(AA test)

by CPST

PS/AB = OS/OB ...(1)

In △CQR and △CAB,

In △CQR and △CAB,

∠RCQ = ∠BCA...(common angle)

∠CRQ = ∠CBA ...(corresponding angles)

△CQR ~ △CAB...(AA test)

by CPST

QR/AB = CR/CB ...(2)

PQRS is a parallelogram

PQRS is a parallelogram

PS = QR,

from (2)

PS/AB = CR/CB ...(3)

From (1) and (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

**Note: Only 1 question will be answered per query**
Answered by Arun | 06 Jul, 2022, 09:13: AM

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