Question

One of the sides of a triangle is divided into segments of $4$ and $6$ units by the point of tangency of the inscribed circle which has radius $2\sqrt{2}$ units, then the largest side of triangle is -

• A. $10$
• B. $\frac{21}{2}$
• C. $\frac{43}{4}$
• D. $11$

Answer 1

The correct option is D $11$


$\tan \left(\frac{A}{2}\right)=\frac{1}{\sqrt{2}}$

$\tan \left(\frac{C}{2}\right)=\frac{\sqrt{2}}{3}$

$\Rightarrow \tan \left(\frac{A+C}{2}\right)=\frac{5}{2\sqrt{2}}$

$\cot \left(\frac{B}{2}\right)=\frac{x}{2\sqrt{2}}=\frac{5}{2\sqrt{2}}$

$x=5$