Question

In a triangle $ABC,$ if $\sin A,\sin B,\sin C$ are in A.P, then

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

Answer 1

Answer: (B)

altitudes are in H.P

$\sin A,\sin B,\sin C$ are in A.P
$\Rightarrow a,b,c$ are in A.P.
$2△=a{h}_1=b{h}_2=c{h}_3$
$\therefore h_1:h_2:h_3=\frac{2△}{a}:\frac{2△}{b}:\frac{2△}{c}$
$=\frac{1}{a}:\frac{1}{b}:\frac{1}{c}$
$\Rightarrow a,b,c$ are in A.P.
$\Rightarrow h_1,h_2,h_3$ are in H.P.