Match the following :
Column-I | Column-II |
(i) In a triangle ABC, if c4 – 2 (a2 + b2) c2 + a4 + a2b2 + b4 = 0 then ∠C= | [A] 120º |
(ii) If the radius of the circumcircle of an isosceles triangle ABC is equal to AB = AC, then the angle A is | [B] 15º |
(iii) In a triangle ABC, angle A is greater than angle B. If the measure of angles A and B satisfy the equation 3 sin x – 4 sin3x = k, 0 < k < 1 then ∠C is equal to | [C] 60º |
(iv) If the hypotenuse of right angled triangle is four times the length of perpendicular drawn from opposite vertex to it, then the difference of the two acute angle will be | [D] 150º |
Text Solution
Verified by Experts(i) [A]; (ii) [A]; (iii) [A]; (iv) [C]
Ans.
(i) [A], [C]
(ii) [A]
(iii) [A]
(iv) [C]
Sol. (i) Given expression can be written as,
(a 2 + b 2 – c 2 ) 2 = a 2 b 2 or, 
= 
or, cos
2 C = 
or, C = 60º or 120º
(ii) We know, 
= 
= 
= 2R
( AB = AC = R, given)
∴ sin B = sin C = 
⇒ B = C = π /6
∴ ∠ A = π – ( π /6 + π /6) = 
(iii) Given, sin 3x = k; …(1)
since A and B satisfy equation (1)
∴ sin 3A = k = sin 3B
or 3A = π – 3B ( A ≠ B)
3(A + B) = π
A + B = 
∴ c = 
(iv) Given BC = 4AD
⇒ a = 4c sin B
⇒ sinA = 4 sin C sin B
⇒ 1 = 2 [cos (C –B) – cos (C + B)]
= cos (C–B) ( cos (B + C) = cos 90º = 0)
∴ C – B = 60º
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