Question

In $\Delta ABC$, if $C={90}^0$, then $R+r=$

• A. $a+b$
• B. $\frac{a+b}{2}$
• C. $b+c$
• D. $\frac{b+c}{2}$

Answer 1

The correct option is B $\frac{a+b}{2}$

$R=\frac{abc}{4\Delta }$

$R=\frac{abc}{4\times \frac{1}{2}ab}$

$R=\frac{c}{2}$

then R+r = $\frac{c}{2}+(s-c)\tan \frac{c}{2}$.....(using the formula of r)

=$\frac{c}{2}+\left(\frac{a+b-c}{2}\right)\tan 45$

=$\frac{a+b}{2}$.