UPSC 2016 CDS I Math Paper

XP

XQ

=

1.5

6

=

1

4

.....(1)

PY

YR

=

2

8

=

1

4

.....(2)
From (1) and (2), we have

XP

XQ

=

PY

YR

In ΔPQR,

XP

XQ

=

PY

YR

∴ XY || QR (Converse of basic proportionality theorem)
In ΔPXY and ΔP RQ
∠PXY = ∠PQR (Corresponding angles)
∠PYX =∠PRQ (Correspondingangles)
∴ ΔPXY ~ ΔPRQ (AA Similarity)
⇒

XY

QR

=

PX

PQ

=

PY

PR

(Corresponding sides are proportional)
⇒

XY

QR

=

1.5

7.5

=

2

10

⇒

XY

QR

=

1

5

⇒QR=5XY