if in a triangle PQR,$\displaystyle \sin P,\sin Q,\sin R$ 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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- Nov 20th 2010, 06:08 AMgrgrsanjayprogression question
if in a triangle PQR,$\displaystyle \sin P,\sin Q,\sin R$ 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 - Nov 22nd 2010, 03:17 AMsa-ri-ga-ma
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?