EXAMPLE 16 If in a A ABC, sin A, sin B and sin C are in AP,then(a) the

1.	EXAMPLE 16 If in a A ABC, sin A, sin B and sin C are in AP,then(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.
Answer» <P>If p 1 ,p 2 ,p 3 , are the ALTITUDES from A, B, C respectively, then Δ= 2 1 ap 2 = 2 1 BP 2 = 2 1 CP 3 ⇒p 1 = a 2Δ ,p 2 = b 2Δ ,p 3 = c 2Δ By the law of sines sinA a = sinB b = SINC c =k(say) ∴= ksinA 2Δ ,p 2 = ksinB 2Δ ,p 3 = ksinC 2Δ Now, sinA,sinB,sinC are in A.P. ⇒p 1 ,p 2 ,p 3 are in H.P.

EXAMPLE 16 If in a A ABC, sin A, sin B and sin C are in AP,then(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.

Answer»

<P>If p

, are the ALTITUDES from A, B, C respectively,

then Δ=

⇒p

2Δ

By the law of sines

sinA

sinB

SINC

=k(say)

∴=

ksinA

2Δ

ksinB

2Δ

ksinC

2Δ

Now, sinA,sinB,sinC are in A.P.

⇒p

are in H.P.

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EXAMPLE 16 If in a A ABC, sin A, sin B and sin C are in AP,then(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.​

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EXAMPLE 16 If in a A ABC, sin A, sin B and sin C are in AP,then(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.