Question

If in a triangle ABC, the altitudes from the vertices upon the opposite sides are in H.P. then sin A, sin B, sin C are in

• A. A.P.
• B. G.P.
• C. F.P.
• D. A.G.S.

Answer 1

The correct option is A A.P.

The three altitudes AD, BE and CF are c $\sin B$, a $\sin C$, b $\sin A$ which are in H.P. or $\sin B\sin C,\sin C\sin A,\sin A\sin B$are in H.P.
or $\frac{1}{\sin B\sin C},\frac{1}{\sin C\sin A},\frac{1}{\sin A\sin B}$ are in A.P.

or $\sin A,\sin B,\sin C$ are in A.P.

We have multiplied each term by $\sin A\sin B\sin C.$