1
AIEEE 2005
+4
-1
In a triangle $$ABC$$, let $$\angle C = {\pi \over 2}$$. If $$r$$ is the inradius and $$R$$ is the circumradius of the triangle $$ABC$$, then $$2(r+R)$$ equals :
A
$$b+c$$
B
$$a+b$$
C
$$a+b+c$$
D
$$c+a$$
2
AIEEE 2004
+4
-1
The sides of a triangle are $$\sin \alpha ,\,\cos \alpha$$ and $$\sqrt {1 + \sin \alpha \cos \alpha }$$ for some $$0 < \alpha < {\pi \over 2}$$. Then the greatest angle of the triangle is :
A
$${150^ \circ }$$
B
$${90^ \circ }$$
C
$${120^ \circ }$$
D
$${60^ \circ }$$
3
AIEEE 2003
+4
-1
The sum of the radii of inscribed and circumscribed circles for an $$n$$ sided regular polygon of side $$a,$$ is :
A
$${a \over 4}\cot \left( {{\pi \over {2n}}} \right)$$
B
$$a\cot \left( {{\pi \over {n}}} \right)$$
C
$${a \over 2}\cot \left( {{\pi \over {2n}}} \right)$$
D
$$a\cot \left( {{\pi \over {2n}}} \right)$$
4
AIEEE 2003
+4
-1
In a triangle $$ABC$$, medians $$AD$$ and $$BE$$ are drawn. If $$AD=4$$,
$$\angle DAB = {\pi \over 6}$$ and $$\angle ABE = {\pi \over 3}$$, then the area of the $$\angle \Delta ABC$$ is :
A
$${{64} \over 3}$$
B
$${8 \over 3}$$
C
$${{16} \over 3}$$
D
$${{32} \over {3\sqrt 3 }}$$
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