Question

Assertion :The statement that circumradius and inradius of a triangle are $12$ and $8$ respectively can not be correct. Reason: circumradius $\ge$ inradius

• A. Both the statements are TRUE and reason is the correct expansion of assertion
• B. Both the statements are TRUE but reason is NOT the correct explanation of assertion
• C. assertion is TRUE and reason is FALSE
• D. assertion is FALSE and reason is TRUE

Answer 1

The correct option is A Both the statements are TRUE and reason is the correct expansion of assertion

$r=4R\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$

but $\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}\in [0,\frac{1}{8}]$

$\Rightarrow r\in (0,\frac{R}{2})\Rightarrow R\ge 2$

$\Rightarrow$ Reason is correct

$\therefore$ If $R=12,r\in (0,6]\Rightarrow r\ne 8$