Match each expression with a value. List I List II (A) λ =(a+b+c)(b+c-a)/(bc) is an integer. Find its greatest possible value. (P) 3 (B) tan A+tan B+tan C=9. Find the minimum of t a n 2 A+ t a n 2 B+

Question

Match each expression with a value. List I List II (A) λ =(a+b+c)(b+c-a)/(bc) is an integer. Find its greatest possible value. (P) 3 (B) tan A+tan B+tan C=9. Find the minimum of t a n 2 A+ t a n 2 B+ t a n 2 C. (Q) approximately 36.3897 (C) Circumcenter O and incenter I satisfy OI∥BC. Find cos B+cos C. (R) 1 (D) a=5,b=4,cos(A-B)=31/32. Find c. (S) 6

TestHub · Accepted Answer

λ =2+2cos A<4, so its largest possible integer is 3. With x=tan A,y=tan B,z=tan C, x+y+z=9 and x+y+z=xyz; optimizing x 2 + y 2 + z 2 gives x=y≈4.250979895,z≈0.498040210 and minimum ≈36.389704. OI∥BC yields r=Rcos A, which gives cos B+cos C=1. Half-angle and cosine rules give c=6 in D.

Mathematics - Properties of Triangle Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(A) $λ$ =(a+b+c)(b+c-a)/(bc) is an integer. Find its greatest possible value.	(P) 3
(B) tan A+tan B+tan C=9. Find the minimum of $t a n^{2}$ A+ $t a n^{2}$ B+ $t a n^{2}$ C.	(Q) approximately 36.3897
(C) Circumcenter O and incenter I satisfy OI∥BC. Find cos B+cos C.	(R) 1
(D) a=5,b=4,cos(A-B)=31/32. Find c.	(S) 6