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Math Help - progression question

  1. #1
    Member grgrsanjay's Avatar
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    Cool progression question

    if in a triangle PQR, \sin P,\sin Q,\sin R are in A.P,then

    which of the following is true
    (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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  2. #2
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    let p,q and r be the sides of the triangle PQR.

    then according the properties of triangle

    p/sinP = q/sinQ = r/sinR = k. So

    p = k*sinP, q = k*sinQ and r = k*sinR. and 2q = p + r

    Let L1, L2 and L3 be the altitudes from P. Q and R points,

    then the area of the triangle PQR is given by

    1/2*p*L1 = 1/2*q*L2 = 1/2*r*L3 = A

    So p = 2A/L1, q = 2A/L2 and r = 2A/L3.

    Now can you proceed?
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