In a `Delta ABC`, the `AM` and `GM` of ex-radii are 8 asnd 4 respectively, then inradius is :

Options

A. `3`
B. `2`
C. `1`
D. `(2)/(3)`

Answer

D

Explanation

In a `Delta aBC`, the …………
Given `AM = 8`
`GM = 4` and Let `HM = H`
We know that, `G^(2)=AH`
`implies H = (G^(2))/(A) = (4^(2))/(8) = 2 implies (3)/((1)/(r_(1))+(1)/(r_(2))+(1)/(r_(3))) = 2`
`implies (3)/((s-a)/(Delta)+(s-b)/(Delta)+(s-c)/(Delta)) = 2`
`implies (3Delta)/(3s-(a+b+c)) = 2 implies (3Delta)/(s) = 2`
`implies 3r = 2 implies r = (2)/(3)`