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Manipal MET2012MathematicsProperties of Triangles

If in a P Q R, P ; Q, R are in A P , then

Options

  1. Athe altitudes are in AP
  2. Bthe altitudes are in HP
  3. Cthe medians are in GP
  4. Dthe medians are in AP

Correct answer

B. the altitudes are in HP

Step-by-step solution

By sine rule array ll & a P = b Q = c R =k Also, & 1 2 a p₁= & 2 a =p₁ & p₁= 2 k P array Similarly, p₁= 2 k Q and p₃= 2 k R Since, P, Q, R are in AP. 1 P 1 Q , 1 R are in H P 2 k P , 2 k Q , 2 k R are in HP p₁, p₂, p₃ are in HP.

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