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Question

If in a ABC, the altitudes from the vertices A,B,C on the opposite side are in HP, then sinA,sinB, and sinC are in


A

HP

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B

Arithmetic – Geometric Progression

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C

AP

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D

GP

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Solution

The correct option is C

AP


Explanation for the correct option:

Find the progression formed by sinA,sinB,sinC.

The area of the triangle is given as: =12h1a=12h2b=12h3c.

So the ratio h1:h2:h3 is given as

h1:h2:h3=2a:2b:2c=1a:1b:1c

Now the altitudes h1,h2,h3 are in HP, so 1a,1b,1c are in HP.

Again as 1a,1b,1c are in HP, so a,b,c are in AP.

Now, as a,b,c are in AP, so using the sine rule asinA=bsinB=csinC it can be said that sinA,sinB,sinC are also in AP.

Hence, the correct option is C.


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