In triangle ABC, `b^(2) sin 2C + c^(2) sin 2B = 2bc` where `b = 20, c = 21`, then inradius =

Monjur Alahi

In triangle ABC, `b^(2) sin 2C + c^(2) sin 2B = 2bc` where `b = 20, c = 21`, then inradius =
A. 4
B. 6
C. 8
D. 9


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

Correct Answer - B
`b^(2) sin 2C + c^(2) sin 2B = 2bc`
`rArr b^(2) (2 sin C cos C) + c^(2) (2 sin B cos B) = 2bc`
`rArr b^(2) (c cos C) + c^(2) (b cos B) = 2Rbc`
`rArr b cos C + c cos B = 2R`
`rArr a = 2R`
`rArr A = 90^(@)`
`:. a^(2) = b^(2) + c^(2) = 400 + 441 = 841`
`rarr a = 29`
Now, `r = (2Delta)/(2s) = (20 xx 21)/(20 + 21 + 29) = (20 xx 21)/(70) = 6`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
Find the principal values of the following (i) `sin^(-1) (sin 1)` (ii) `sin^(-1) (sin 2)` (iii) `sin^(-1) (sin 10)` (iv) `sin^(-1) (sin 20)` (v) `sin^

(i) Since `1 in [-pi//2, pi//2], sin^(-1) (sin 1) = 1` (ii) Since `2 in [-pi//2, pi//2], sin^(-1) (sin 2) != 2` `:. Sin^(-1) (sin 2) = sin^(-1) (sin (pi)...

2 Answers 1 views
`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 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 an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio

Correct Answer - B We have `Delta = (sqrt3)/(4) a^(2), s = (3a)/(2)` `:. r = (Delta)/(s) = (a)/(2sqrt3), R = (abc)/(4Delta) = (a^(3))/(sqrt3 a^(2)) = (a)/(sqrt3)` and `r_(1) = (Delta)/(s-a)...

2 Answers 1 views
If two sides of a triangle are roots of the equation `x^(2) -7x + 8 = 0` and the angle between these sides is `60^(@)` then the product of inradius an

Correct Answer - B Let a and b the roots of `x^(2) -7 x + 8 = 0` Then `a + b = 7, ab = 8` Also, `C = 60^(@)`...

2 Answers 1 views
The inradius in a right angled triangle with integer sides is r If r = 4, the greatest perimeter (in units) is

Correct Answer - B Let a, b and `c(a lt b ltc)` be the sides of given triangle. Also, `2r = a + b - c` ltbr when `r = 4`...

2 Answers 3 views
In triangle ABC, `sinA sin B + sin B sin C + sin C sin A = 9//4 and a = 2`, then the value of `sqrt3 Delta`, where `Delta` is the area of triangle, is

Correct Answer - 3 The given equation is `4 sin A sin B + 4 sin B sin C + 4 sin C sin A = 9` `rArr 2 cos (A...

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