A to Z Exams

In ΔABC, R2 (sin 2A+sin 2B+sin 2C)=

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

In ΔABC, if A=900 then r2 +r3 =

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

In ΔABC, r12+r22+r32+r2 =

A man observes that angle of elevation of the top of a tower from a point P on the ground is θ. He moves a certain distance towards the foot of the tower and finds that the angle of elevation of the top has doubled. He further moves a distance 3/4 of the previous and finds that the angle of elevation is three times that at P. Then angle θ is given by

If sin A= sin2 B and 2 cos2 A =3 cos2 B, then the ΔABC is

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

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

In a triangle ABC, (a2-b2-c2) tan A+ (a2-b2+c2) tan B is equal to

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

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

In ΔABC, (r1 +r2) (r2 +r3) (r3+r1) =

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

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

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

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

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

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

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

If a. cos (θ+ α)= b cos (θ-α), then (a+b) tan θ=

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

In ΔABC, if b=c=R then A=

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

If α,β are solutions of a cos 2θ+b sin 2θ=c, then tan α tan β=

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

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

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

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

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) =