If in a `!ABC` , sin A, sin B and sin C are in A.P, then

Options

A. the altitudes are in A.P.
B. the altitudes are in H.P.
C. the medians are in G.P.
D. the medians are in A.P.

Explanation

Let `p_(1), p_(2), p_(3)` be the altitudes of `Delta` ABC. Then,
`Delta=1/2ap_(1)=1/2bp_(2)=1/2cp_(3)`
`rArra=(2Delta)/(p_(1)).b=(2Delta)/(p_(2)),c=(2Delta)/(p_(3))`

Now,
sin A, sin B, sin C are in AP.
`rArra,b,c` are in A.P.
`rArr(2Delta)/(p_(1)),(2Delta)/(p_(2)),(2Delta)/(p_(3))` are in A.P.
`rArr1/(p_(1)),1/(p_(2)),1/(p_(3))` are in A.P. `rArrp_(1),p_(2),p_(3)` are in H.P.