IIT-JEE 2006 | Properties of Triangle Question 18 | Mathematics

IIT-JEE 2006

MCQ (More than One Correct Answer)

-1

Internal bisector of $\angle A$ of triangle $A B C$ meets side BC at D . A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F . If $a, b, c$ represent sides of $\triangle \mathrm{ABC}$ then

AE is HM of $b$ and $c$

$\mathrm{AD}=\frac{2 b c}{b+c} \cos \frac{\mathrm{~A}}{2}$

$\mathrm{EF}=\frac{4 b c}{b+c} \sin \frac{\mathrm{~A}}{2}$

the triangle AEF is isosceles

IIT-JEE 1987

MCQ (More than One Correct Answer)

-0.5

In a triangle, the lengths of the two larger sides are $$10$$ and $$9$$, respectively. If the angles are in $$AP$$. Then the length of the third side can be

$$5 - \sqrt 6 $$

$$3\sqrt 3 $$

$$5$$

$$5 + \sqrt 6 $$

IIT-JEE 1986

MCQ (More than One Correct Answer)

-0.5

There exists a triangle $$ABC$$ satisfying the conditions

$$b\sin A = a,A < \pi /2$$

$$b\sin A > a,A > \pi /2$$

$$b\sin A > a,A < \pi /2$$

$$b\sin A < a,A < \pi /2,b > a$$

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