Properties of Triangles 1 Question 10

10. If in a PQR,sinP,sinQ,sinR are in AP, then

(a) the altitudes are in AP

(1998, 2M)

(b) the altitudes are in HP

(c) the medians are in GP

(d) the medians are in AP

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Answer:

Correct Answer: 10. (b, c)

Solution:

  1. By the law of sine rule,

asinP=bsinQ=csinR=k

Also,

12ap1=Δ

2Δa=p1p1=2ΔksinP

Similarly, p2=2ΔksinQ and p3=2ΔksinR

Since, sinP,sinQ and sinR are in AP, hence p1,p2,p3 are in HP.



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