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Properties of Triangles Practice Questions - DPP for JEE

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 Page 3


From (i) and (ii),
– 100 = h (cot 3a – cot 2a),
From (ii) and (iii),
– 200 = h (cot 2a – cot a),
or
or
Hence, m
4. (b)
= 
= 
? sin
2
A + sin
2
B + sin
2
C – 2cos A cos B cos C = 2
Page 4


From (i) and (ii),
– 100 = h (cot 3a – cot 2a),
From (ii) and (iii),
– 200 = h (cot 2a – cot a),
or
or
Hence, m
4. (b)
= 
= 
? sin
2
A + sin
2
B + sin
2
C – 2cos A cos B cos C = 2
5. (b)
Diameter 
6. (d) Consider a ?ABC with sides a, b, c then by cosine formula, we
have
But given  2b
2
 = a
2
 + c
2
 
  = 
Consider 
= 3 – 4 sin
2
 B = 3 – 4 (1 – cos
2
 B) = – 1 + 4 cos
2
 B
 
Page 5


From (i) and (ii),
– 100 = h (cot 3a – cot 2a),
From (ii) and (iii),
– 200 = h (cot 2a – cot a),
or
or
Hence, m
4. (b)
= 
= 
? sin
2
A + sin
2
B + sin
2
C – 2cos A cos B cos C = 2
5. (b)
Diameter 
6. (d) Consider a ?ABC with sides a, b, c then by cosine formula, we
have
But given  2b
2
 = a
2
 + c
2
 
  = 
Consider 
= 3 – 4 sin
2
 B = 3 – 4 (1 – cos
2
 B) = – 1 + 4 cos
2
 B
 
.
7. (d) From 
From 
Distance between the men = 
8. (b) From the given figure we have
 and 
 
? ?
? or 60 m
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