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MHT CET20239 May 2023Evening ShiftMathematicsProperties of TrianglesActual

In PQR , P , Q and R are in A.P., then

Options

  1. Aits altitudes are in A.P.
  2. Bits altitudes are in H.P.
  3. Cits medians are in G.P.
  4. Dits medians are in A.P.

Correct answer

B. its altitudes are in H.P.

Step-by-step solution

Let p ₁, p ₂, p ₃ be the altitudes of PQR Area of P Q R aligned & = 1 2 base height & = 1 2 p ₁ a aligned Area = 1 2 p ₁ a array ll & p ₁=2 Area a ... (i) & similarly, & p ₂= 2 Area b ... (ii) & p ₃= 2 Area c ... (iii) array By sine Rule, a P = b Q = c R Let a P = b Q = c R =k P= a k , Q= b k , R= c k P, Q and R are in A.P. a , b , c are in A.P. 1 a , 1 b , 1 c are in H.P. ... (iv) From equations (i), (ii), (iii) and (iv), we get p ₁, p ₂ and p ₃ are in H.P.

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