Match the following :
For Δ ABC, a, b, c, s, r, R have their usual meanings
Column-I | Column-II |
(i) If b cos2+ a cos2= , where a =, b = 1 then c is greater than | [A] |
(ii) R = and r = then k must be greater than | [B] 1 |
(iii) Circumcentre is at origin and a ≤ sin A. P(x, y) lie inside the circumcircle and k = , then k must be greater than | [C] |
(iv) ‘G’ is centroid and angle between and are obtuse then a2 is greater than (b = , c = ) | [D] 2 |
Text Solution
Verified by Experts(i) [A]; (ii) [D]; (iii) [A]; (iv) [A]
Ans.
(i) [A], [B]
(ii) [D]
(iii) [A], [B]
(iv) [A], [B]
Sol. (i) 
(a + b + c) = 
⇒ c = 
(ii) ∠ ∠ A = 90º also rk = c = r 
⇒ (k – 1) > cot45º
⇒ k > 2
(iii) R ≤ 
⇒ x 2 + y 2 < 
⇒ | xy | < 
⇒ k > 1
(iv) Let 
< 0
⇒ (2p 2 + 
> 0
⇒ 5a 2 > c 2 + b 2
⇒ a 2 > 1
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