In triangle ABC, match each expression with its value. List I List II (A) If (s-a)/11=(s-b)/12=(s-c)/13, find 33 t a n 2 (A/2). (P) 6 (B) If a=5,b=4,cos(A-B)=31/32, find c. (Q) 52 (C) If OH∥BC, O circ

Question

In triangle ABC, match each expression with its value. List I List II (A) If (s-a)/11=(s-b)/12=(s-c)/13, find 33 t a n 2 (A/2). (P) 6 (B) If a=5,b=4,cos(A-B)=31/32, find c. (Q) 52 (C) If OH∥BC, O circumcenter and H orthocenter, find 4 t a n 2 B t a n 2 C. (R) 26 (D) If R=12,r=4, find the sum of exradii. (S) 13 (T) 36

TestHub · Accepted Answer

Put s-a=11k,s-b=12k,s-c=13k, hence s=36k and 33 t a n 2 (A/2)=13. Half-angle and cosine rules give c=6 in B. For C, OH∥BC implies tan B tan C=3, so 4 t a n 2 B t a n 2 C=36. Finally r a ​ + r b ​ + r c ​ =r+4R=52.

Mathematics - Properties of Triangle Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(A) If (s-a)/11=(s-b)/12=(s-c)/13, find $33 t a n^{2}$ (A/2).	(P) 6
(B) If a=5,b=4,cos(A-B)=31/32, find c.	(Q) 52
(C) If OH∥BC, O circumcenter and H orthocenter, find $4 t a n^{2}$ B $t a n^{2}$ C.	(R) 26
(D) If R=12,r=4, find the sum of exradii.	(S) 13
	(T) 36