The correct options are
A 4 units
D 2 units
Use the relation between 'r' and 'R' for any triangle.
r=4RsinA2sinB2sinC2=2RsinA2(cosB−C2−cosB+C2)=2RsinA2(cosB−C2−sinA2)....(1)
Given that a=12 and R=10. So we get sinA=a2R=35
⇒cosA=45
⇒sinA2=√1−cosA2=1√10....(2)
From (1) and (2), r will be maximum when cosB−C2 takes maximum value, which is 1.
So, we get maximum value of r=2×10×1√10(1−1√10)=2(√10−1)
Since 3<√10<3.2, we get maximum value of r is such that 4<rmax<4.4
So any possible value of r has to be less than rmax.
4 and 2 are possible.