Properties of Triangles

If sin A,sin B,sin C are in A.P.
prove that the altitudes are in H.P .

1 Answers

2305

Shaswata Roy ·Jan 24 at 7:05

Let's denote area by Î”.

$sin A, sin B, sin C a r e i n A P$

$\to 2 R sin A, 2 R sin B, 2 R sin C a r e i n A P$

$\to a, b, c a r e i n A P$

$\to a 1 , b 1 , c 1 a r e i n H P$

$\to a 2 Δ , b 2 Δ , c 2 Δ a r e i n H P$

$\to h a , h b , h c a r e i n H P$

Where h_a,h_b,h_c are the altitudes of the triangle.

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