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UPSC CDS Math Triangles Questions
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© examsnet.com
Question : 29
Total: 68
The diagonals of a cyclic quadrilateral ABCD intersect at P and the area of the triangle APB is 24 square cm. If AB = 8 cm and CD = 5 cm,then what is the area of the triangle CPD ?
[2017 CDS-II]
24 square cm
15 square cm
12.5 square cm
9.375 square cm
Validate
Solution:
The diagonals AC and BD intersect at P.
∴ AP × PC =PB × PD
⇒
A
P
P
B
=
P
D
P
C
⇒
A
P
P
B
=
P
D
P
C
In ΔAPB and ΔCPD
A
P
P
B
=
P
D
P
C
∠APB = ∠CPD (Vertically opposite angles)
∴ ΔAPB~ ΔCPD (SAS Similarity)
⇒
a
r
(
Δ
A
P
B
)
a
r
(
Δ
C
P
D
)
=
A
B
2
C
D
2
(Area theorem)
⇒
a
r
(
Δ
C
P
D
)
=
24
×
25
64
=
9.375
c
m
2
© examsnet.com
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