Question

In a $△ABC$, $\tan A$ and $\tan B$ are the roots of $pq(x^2+1)=r^{2}x$. Then $△ABC$ is

• A. a right angled triangle
• B. an acute angled triangle
• C. an obtuse angled triangle
• D. an equilateral triangle

Answer 1

The correct option is A a right angled triangle

$\tan A+\tan B=\frac{r^2}{pq}\tan A\tan B=1\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}\tan (A+B)=\frac{\frac{r^2}{pq}}{1-1}=\infty A+B={90}^{\circ }A+B+C={180}^{\circ }\Rightarrow C={90}^{\circ }$

One of the angle is right angle so the triangle is Right angled triangle.