Match the following quantities. List I List II (A) Integer p satisfying p 2 -2p cos x=673 and tan(x/2)=7. (P) 8 (B) Maximum of (sin θ +cos θ )². (Q) 9 (C) P is circumcenter of acute ABC. Circles with

Question

Match the following quantities. List I List II (A) Integer p satisfying p 2 -2p cos x=673 and tan(x/2)=7. (P) 8 (B) Maximum of (sin θ +cos θ )². (Q) 9 (C) P is circumcenter of acute ABC. Circles with altitudes PD, PE, PF of triangles PBC, PCA, PAB as diameters have radii r 1 ​ , r 2 ​ , r 3 ​ . Minimum of ( a 2 / r 1 2 ​ + b 2 / r 2 2 ​ + c 2 / r 3 2 ​ )/18. (R) 2 (D) If a=6,b=3 and cos(A-B)=4/5, find area of ABC. (S) 25

TestHub · Accepted Answer

cos x=-24/25, so the positive integer solution in A is 25. B is 2 at θ =45°. For C, a/ r 1 ​ =4tan A and cyclically; ∑ t a n 2 A≥9 in an acute triangle, hence the expression is at least 16·9/18=8. In D, the half-angle identity gives C=90°, so area=ab/2=9.

Mathematics - Properties of Triangle Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(A) Integer p satisfying $p^{2}$ -2p cos x=673 and tan(x/2)=7.	(P) 8
(B) Maximum of (sin $θ$ +cos $θ$ )².	(Q) 9
(C) P is circumcenter of acute ABC. Circles with altitudes PD, PE, PF of triangles PBC, PCA, PAB as diameters have radii $r_{1}$ , $r_{2}$ , $r_{3}$ . Minimum of ( $a^{2}$ / $r_{1}^{2}$ + $b^{2}$ / $r_{2}^{2}$ + $c^{2}$ / $r_{3}^{2}$ )/18.	(R) 2
(D) If a=6,b=3 and cos(A-B)=4/5, find area of ABC.	(S) 25