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CAT Exam Model Paper 4 with solutions for free online practice
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© examsnet.com
Question : 14
Total: 60
In the given figure AB is the diameter of a circle with center ‘O’. C is any point in the circle such that ∠ACB = 120°. OD is perpendicular to BC and the length of OD is 1.5 cm.
What is the length of AC (in cm)?
3
√
3
2
3
√
3
2
√
3
6
Validate
Solution:
Construction:
Extend BC to cut the circle at E and join AE.
∆AEB is right angled at E. (Angle in a semicircle is a right angle).
Hence, both AE and OD are perpendicular to EB. By AA property:
∆AEB -∆ODB
Hence,
O
B
A
B
=
O
D
A
E
or
O
D
A
E
=
1
2
⇒ AE = 2OD = 3cm
In right ∆AEC:
∠ACE = 180° ∠ACB - 180° -120° = 60°
and
A
C
=
A
E
sin
60
°
=
3
(
2
√
3
)
=
2
√
3
cm
© examsnet.com
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