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UPSC CDS Math Triangles Questions
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© examsnet.com
Question : 40
Total: 68
In a triangle
P
Q
R
, point
X
is on
P
Q
and point
Y
is on
P
R
such that
X
P
=
1.5
units,
X
Q
=
6
units,
P
Y
=
2
units and
Y
R
=
8
units. Which of the following are correct?
1.
Q
R
=
5
X
Y
2.
Q
R
is parallel to
X
Y
.
3. Triangle
P
Y
X
is similar to triangle PRQ.
Select the correct answer using the code given below.
[2016 CDS-I]
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
Validate
Solution:
X
P
X
Q
=
1.5
6
=
1
4
.....(1)
P
Y
Y
R
=
2
8
=
1
4
.....(2)
From (1) and (2), we have
X
P
X
Q
=
P
Y
Y
R
In ΔPQR,
X
P
X
Q
=
P
Y
Y
R
∴ XY || QR (Converse of basic proportionality theorem)
In ΔPXY and ΔP RQ
∠PXY = ∠PQR (Corresponding angles)
∠PYX =∠PRQ (Correspondingangles)
∴ ΔPXY ~ ΔPRQ (AA Similarity)
⇒
X
Y
Q
R
=
P
X
P
Q
=
P
Y
P
R
(Corresponding sides are proportional)
⇒
X
Y
Q
R
=
1.5
7.5
=
2
10
⇒
X
Y
Q
R
=
1
5
⇒
Q
R
=
5
X
Y
© examsnet.com
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