If in a triangle A B C,(s-a)(s-b)=s(s-c), then angle C is equal t…

MCQ

If in a triangle $A B C,(s-a)(s-b)=s(s-c)$, then angle $C$ is equal to

✓
$90^{\circ}$
B
$45^{\circ}$
C
$30^{\circ}$
D
$60^{\circ}$

✓

Answer

Correct option: A.

$90^{\circ}$

(A) $\tan \frac{C}{2}=\sqrt{\frac{(s-a)(s-b)}{s(s-c)}}=1$
$\Rightarrow \tan \frac{ C }{2}=\tan 45^{\circ} \Rightarrow \frac{ C }{2}=45^{\circ}$
$\Rightarrow C=90^{\circ}$

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