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UPSC CDS Math Quadrilateral and Polygon Questions
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© examsnet.com
Question : 41
Total: 41
AB is a straight line; C and D are points on the same side of AB such that AC is perpendicular to AB and DB is perpendicular to AB. Let AD and BC meet at E.
what is
A
E
A
D
+
B
E
B
C
equal to ?
[2014 CDS-I]
2
1.5
1
None of the above
Validate
Solution:
In ΔAEF and ΔABD,
∠
E
A
F
=
∠
D
A
B
(Common)
∠
A
F
E
=
∠
A
D
B
(90°)
∴
Δ
AEF
~
Δ
ABD
(AA Similarly)
⇒
A
E
A
D
=
E
F
B
D
=
A
F
A
B
......(1)
Similarly,
Δ
BEF
~
Δ
BAC
(AA Similarity)
∴
B
E
B
C
=
E
F
C
A
=
B
F
A
B
.....(2)
Adding (1) and (2), we have
A
E
A
D
+
B
E
B
C
=
A
F
A
B
+
B
F
A
B
=
A
F
+
B
F
A
B
=
A
B
A
B
=
1
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