In A B C if A B C>0, then the triangle is - Vidyadip

MCQ

In $\triangle A B C$ if $\cot A \cot B \cot C>0$, then the triangle is

✓
acute-angled
B
right-angled
C
obtuse-angled
D
isosceles right-angled

✓

Answer

Correct option: A.

acute-angled

(a) acute angled
Hint:
$\cot A \cot B \cot C>0$
Case I:
$\cot A, \cot B, \cot C>0$
$\therefore \cot A>0, \cot B>0, \cot C>0$
$\therefore 0<A<\frac{\pi}{2}, 0<B<\frac{\pi}{2}, 0<C<\frac{\pi}{2}$
$\therefore \triangle \mathrm{ABC}$ is an acute angled triangle.
Case II:
Two of $\cot A, \cot B, \cot C<0$
$0<A, B, C<\pi$ and two of $\cot A, \cot B, \cot C<0$
$\therefore$ Two angles $A_t B_t C$ are in the 2nd quadrant which is not possible.

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