Match the progression statements. List I List II (A) Altitudes are in HP; the corresponding angle sines are ... (P) in AP (B) Exradii are in HP; the corresponding sides are ... (Q) in HP (C) If H A 2

Question

Match the progression statements. List I List II (A) Altitudes are in HP; the corresponding angle sines are ... (P) in AP (B) Exradii are in HP; the corresponding sides are ... (Q) in HP (C) If H A 2 , H B 2 , H C 2 are in AP for orthocenter H, then a 2 , b 2 , c 2 are ... (R) in GP (D) Angles A,B,C are in AP; a 2 , b 2 /2, c 2 are ... (S) not in AP

TestHub · Accepted Answer

Altitudes are inversely proportional to side lengths, giving A. Reciprocal exradii are proportional to s-a,s-b,s-c, giving B. H A 2 = 4 R 2 co s 2 A gives C. For D, B=60°, and the proposed square AP would require b 2 = a 2 + c 2 , contrary to b 2 = a 2 + c 2 -ac.

Mathematics - Properties of Triangle Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(A) Altitudes are in HP; the corresponding angle sines are ...	(P) in AP
(B) Exradii are in HP; the corresponding sides are ...	(Q) in HP
(C) If $H A^{2}$ , $H B^{2}$ , $H C^{2}$ are in AP for orthocenter H, then $a^{2}$ , $b^{2}$ , $c^{2}$ are ...	(R) in GP
(D) Angles A,B,C are in AP; $a^{2}$ , $b^{2}$ /2, $c^{2}$ are ...	(S) not in AP