If in a triangle ABC, `(1 + cos A)/(a) + (1 + cos B)/(b) + (1+ cos C)/(c) = (k^(2) (1 + cos A) (1 + cos B) (1 + cos C))/(abc)`, then k is equal to

Monjur Alahi

If in a triangle ABC, `(1 + cos A)/(a) + (1 + cos B)/(b) + (1+ cos C)/(c) = (k^(2) (1 + cos A) (1 + cos B) (1 + cos C))/(abc)`, then k is equal to
A. `(1)/(2 sqrt2R)`
B. 2R
C. `(1)/(R)`
D. none of these


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

Correct Answer - B
`L.H.S. = (1 + cos A)/(a) + (1 + cos B)/(b) + (1 + cos C)/(c)`
`= (2 cos^(2).(A)/(2))/(2R sin A) + (2 cos^(2).(B)/(2))/(2R sin B) + (2 cos^(2).(C)/(2))/(2R sin C)`
`= (1)/(2R) (cot.(A)/(2) + cot.(B)/(2) + cot.(C)/(2))`
Now, `(1 + cos A)/(a) .(1 + cos B)/(b) .(1 + cos C)/(c)`
`= (cos^(2).(A)/(2))/(R sin A).(cos^(2).(B)/(2))/(R sin B) .(cos^(2)/(C)/(2))/(R sin C)`
`= (1)/(8R^(3)) cot.(A)/(2) cot.(B)/(2) cot.(C)/(2)`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
`A (veca), B (vecb) and C (vecc)` are the vertices of triangle ABC and `R(vecr)` is any point in the plane of triangle ABC, then `vecr, (veca xx vecb

Correct Answer - b A vector perpendicular to the plane of ` A(veca) , B(vecb) and C(vecc)` is `(vecb -veca) xx (vecc-veca) = vecaxxvecb +vecb xx vecc +vecc xx veca` Now...

2 Answers 1 views
Each side of triangle ABC is divided into three equal parts. Find the ratio of the are of hexagon `P Q R S T U` to the area of the triangle ABC.

Area of hexagon PQRSTU `Delta_(1) = " area of " Delta ABC - " area of " Delta APQ - " area of " Delta BTU - " area of...

2 Answers 1 views
In a triangle ABC, AD is the altitude from A. If `b gt c`. `angleC = 23^(@) and AD = (abc)/(b^(2) - c^(2), " then " angle B =`

Correct Answer - C `Delta = (1)/(2) a xx AD` `rArr AD = (2Delta)/(a) = (abc)/(b^(2) -c^(2))` (given) `rArr (2Delta)/(a) = (4R.Delta)/(b^(2) -c^(2))` `rArr 2Ra = b^(2) -c^(2)` `rArr sin A...

2 Answers 1 views
With usual notations, in triangle ABC, `a cos (B - C) + b cos (C - A) + c cos (A - B)` is equal to

Correct Answer - A `a cos (B -C) + b cos (C -A) + c co s(A -B)` `2R sin A co s(B -C) + 2R sin B cos (C -...

2 Answers 2 views
If in `Delta ABC, 8R^(2) = a^(2) + b^(2) + c^(2)`, then the triangle ABC is

Correct Answer - A We have `8R^(2) = a^(2) + b^(2) + c^(2)` `4 R^(2) (sin^(2) A + sin^(2) B + sin^(2)C)` or `sin^(2) A + sin^(2)B + sin^(2)C = 2`...

2 Answers 1 views
In triangle ABC, `R (b + c) = a sqrt(bc)`, where R is the circumradius of the triangle. Then the triangle is

Correct Answer - C `R(b +c) = a sqrt(bc) = 2R sin A sqrt(bc)` `:. sin A = (b +c)/(2sqrt(bc))` Now `sin A le 1` `rArr (b + c)/(2sqrt(bc)) le 1`...

2 Answers 1 views
In triangle ABC, let `angle C = pi//2`. If r is the inradius and R is circumradius of the triangle, then `2(r + R)` is equal to

Correct Answer - A Since `DeltaABC` is right angled at C, circum-radius, `R = (c)/(2)` Now, `r = (s -c) tan (C//2) = (s-c) tan (pi//4) = s -c` Thus, `2(r...

2 Answers 1 views
In triangle ABC, the line joining the circumcenter and incenter is parallel to side AC, then `cos A + cos C` is equal to

Correct Answer - B The distance of circumcenter from side AC is `R cos B`, and the distance of incenter from side AC is r. Therefore, `R = cos B =...

2 Answers 3 views
If `R_(1)` is the circumradius of the pedal triangle of a given triangle ABC, and `R_(2)` is the circumradius of the pedal triangle of the pedal trian

Correct Answer - B Circumradius of triangle ABC, R = 5 `:.` Circumradius of pedal triangle, `R_(1) = 5//2` and so on. Now, `underset(i=1)overset(oo)sum R_(i) + R_(1) + R_(2) + R_(3)...

2 Answers 1 views
Each side of an equilateral triand 12 is \( 24 cm \) the mid - point of its sides are joined to form another tranpla this brress is doins centinuously infinite 46. The perimeter of 7 th triangle is \( ( \) in \( cm ) \) a) \( \frac{3}{4} \) b) \( \frac{5}{8} \) c) \( \frac{9}{8} \) d) \( \frac{7}{8} \) 47. The sum of perimeter of all triangle is (in \( cm \) ) a) 144 b) 625 c) 400 d) 169 48. The area of all the triangle is (in sq cm) a) 576 b) \( 144 \sqrt{3} \) c) \( 169 \sqrt{3} \) d) \( 192 \sqrt{3} \) 49. The sum of perimeter of first 6 triangle is (in \( cm \) ) a) 120 b) \( \frac{567}{4} \) c) \( \frac{569}{4} \) d) 144 50. The side of the 5th triangle is (in \( cm \) ) a) 6 b) \( 1.5 \) c) \( 0.75 \) d) 3

post the question correctly

2 Answers 1 views
X