### Eamcet - Maths - Solutions Of Triangles

If, in aΔABC, r3=r1+r2+r , then ‹A+‹B is equal to

A.  1200

B.  1000

C.  900

D.  800

90<sup>0</sup>

Explanation :
No Explanation available for this question

In ΔABC, if b=c=R then A=

A.  300

B.  600

C.  900

D.  1200

600

Explanation :
No Explanation available for this question

In ΔABC, if r1,r2,r3 are in H.P, then a, b, c are in

A.  A.P

B.  G.P

C.  H.P

D.  none

A.P

Explanation :
No Explanation available for this question

I: In a ΔABC, if 4s(s-a) (s-b) (s-c) =a2b2 then it is right angled triangle II: In a ΔABC, if sin A+ sin B +sin C maximum then triangle is equilateral

A.  only I is true

B.  only II is true

C.  both I,II are true

D.  neither I and II is true

both I,II are true

Explanation :
No Explanation available for this question

In ΔABC, if cos A cos B +sin A sin B sin C =1, then a:b:c =

A.  1:1:1

B.  1:2:√2

C.  1:2:2

D.  1:1:√2

1:1:√2

Explanation :
No Explanation available for this question

If 4,5 are two sides of a triangle and the included angle is 600, then is area is

A.  3

B.  5

C.  5√3

D.  3√3

5√3

Explanation :
No Explanation available for this question

In ΔABC, if r1 =3, r2= 10, r3= 15, then c=

A.  5

B.  12

C.  13

D.  13/2

13

Explanation :
No Explanation available for this question

.In ΔABC, if 2R+ r= r1, then the triangle isa

A.  isosceles

B.  equilatcral

C.  right angled

D.  none

right angled

Explanation :
No Explanation available for this question

If sin(y+z-x),sin(z+x-y), sin(x+y-z) are in A.P then tan x, tan y, tan z are in

A.  A.P

B.  G.P

C.  H.P

D.  A.G.P

A.P

Explanation :
No Explanation available for this question

If Two angles of a triangle are 300, 450 and the included side is √3+1, then the remaining sides are

A.  2,√2

B.  2,2√3

C.  √2,4

D.  2,4√3

2,√2

Explanation :
No Explanation available for this question

In ΔABC, if (a+b-c) (a+b-c) = 3ab, then C =

A.  600

B.  300

C.  900

D.  none

600

Explanation :
No Explanation available for this question

In ΔABC, if a= 26, b=30, cos C=63/65 then  r1:r2:r3 =

A.  4:12:1

B.  3:4:12

C.  1:4:12

D.  4:12:3

4:12:1

Explanation :
No Explanation available for this question

In ΔABC, if a,b,c are in A.P. the greatest angle is A and least is C then 4(1- cos A) (1-cos C) =

A.  cos A + cos C

B.  cos A – cos C

C.  sin A + sin C

D.  cos A – sin C

cos A + cos C

Explanation :
No Explanation available for this question

If a, b, c are the sides of a triangle then the range of ab+bc+ca/a2+b2+c2 is

A.  [1, 2]

B.  (1/2, 1]

C.  [1/2, 2)

D.  (-1/2, 2)

(1/2, 1]

Explanation :
No Explanation available for this question

If (a+b)2 = c2+ab in a ΔABC and if √2 (sin A+ cos A) =√3 then ascending order of angles A,B,C is

A.  A, B, C

B.  A, C, B

C.  B, A, C

D.  C, B, A

A, C, B

Explanation :
No Explanation available for this question

In ΔABC, (r1 +r2) (r2 +r3) (r3+r1) =

A.  4Rs2

B.  4Rr2

C.  R

D.  0

4Rs2

Explanation :
No Explanation available for this question

In ΔABC , if a=7, b=7√3 and right angled at C, then c=

A.  2√3

B.  √21

C.  8

D.  14

14

Explanation :
No Explanation available for this question

If α, β are solutions of a tan θ+b sec θ=c then tan (α+β) =

A.  2ac/a2-c2

B.  2ac/c2-a2

C.  2ac/a2+c2

D.  none

2ac/a2-c2

Explanation :
No Explanation available for this question

If I1,I2,I3 are excentres of the triangle with vertices (0,0), (5,12), (16,12) then the orthocentre of ?I1,I2,I3 is

A.  (6,9)

B.  (7,9)

C.  (6,7)

D.  (9,7)

(7,9)

Explanation :
No Explanation available for this question

An observer finds that the angular elevation of a tower is θ. On advancing ‘a’ metres towards the tower, the elevation is 450 and on advancing b metres the elevation is 900-θ. The height of the tower is

A.  ab/(a+b)metres

B.  ab/(a-b)

C.  (a-b)/ab

D.  (a+b)/ab

ab/(a-b)

Explanation :
No Explanation available for this question

A vertical tower stands on a declivity which is included at 150 to the horizon. From the foot of the tower a man ascends the declivity for 80 feet and then finds that the tower subtends an angle of 300. The height of the tower is

A.  20 (√6 - √2)

B.  40 (√6 - √2)

C.  40 (√6 + √2)

D.  none

40 (√6 - √2)

Explanation :
No Explanation available for this question

In ΔABC , if c2= a2+b2, 2s= a+b+c, then 4s (s-a) (s-b) (s-c) =

A.  s4

B.  b2c2

C.  c2a2

D.  a2b2

a2b2

Explanation :
No Explanation available for this question

In a triangle ABC, if cot A = (x3+x2+x)1/2, cot B= (x+x-1+1)1/2 and cot C= (x-3+x-2+x-1) -1/2 then the triangle is

A.  isosceles

B.  obtuse angled

C.  right angled

D.  none

right angled

Explanation :
No Explanation available for this question

If A=(1,1) ,B=(4,5) and C=(6,13) then cos A=

A.  64/63

B.  63/65

C.  56/36

D.  36/56

63/65

Explanation :
No Explanation available for this question

In ΔABC , if A=750, B=450, C=√3, then b=

A.  2

B.  √3

C.  2√3

D.  √2

√2

Explanation :
No Explanation available for this question

In ΔABC, if a(b cos C + c cos B) =2ka2, then k =

A.  0

B.  1

C.  1/2

D.  2

1/2

Explanation :
No Explanation available for this question

In ΔABC, R2 (sin 2A+sin 2B+sin 2C)=

A.  Δ

B.  3Δ

C.  2Δ

D.  4Δ

Explanation :
No Explanation available for this question

In ΔABC, if cos2 A+cos2B+ cos2C=3/4, then the triangle is

A.  right angled

B.  equilateral

C.  isosceles

D.  none

equilateral

Explanation :
No Explanation available for this question

The angle of elevation of the summit of a mountain at a point A is 450. After walking 200 mt from A towards the mountain along a road included at 150, it is observed that the angle of elevation of the summit is 600. The height of the mountain is

A.  100 (√6 +√2) mt

B.  100 (√6 -√2) mt

C.  100/√6 mt

D.  100/√2 mt

100 (√6 +√2) mt

Explanation :
No Explanation available for this question

In ΔABC, if sin A: sin C = sin (A-B) :sin (B-C), then a2,b2,c2 are in

A.  A.P

B.  H.P

C.  G.P

D.  none