Home
Class 12
MATHS
Vertices of a variable acute angled tria...

Vertices of a variable acute angled triangle `A B C` lies on a fixed circle. Also, `a ,b ,ca n dA ,B ,C` are lengths of sides and angles of triangle `A B C ,` respectively. If `x_1, x_2a n dx_3` are distances of orthocenter from `A ,Ba n dC ,` respectively, then the maximum value of `((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c))` is `-sqrt(3)` b. `-3sqrt(3)` c. `sqrt(3)` d. `3sqrt(3)`

Promotional Banner

Similar Questions

Explore conceptually related problems

Vertices of a variable acute angled triangle ABC lies on a fixed circle. Also a, b, c and A, B, C are lengths of sides and angles of triangle ABC, respectively. If x_(1),x_(2) and x_(3) are distances of orthocentre from A, B and C, respectively, then the maximum value of ((dx_(1))/(da)+(dx_(2))/(db)+(dx_(3))/(dc)) is

If x=1+1/(3+1/(2+1/(3+1/(2oo)))) a sqrt(5/2) b. sqrt(3/2) c. sqrt(7/3) d. sqrt(5/3)

The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4 is a. sqrt(30) b. 2sqrt(30) c. 5sqrt(30) d. 3sqrt(30)

If the angle A ,Ba n dC of a triangle are in an arithmetic propression and if a , ba n dc denote the lengths of the sides opposite to A ,Ba n dC respectively, then the value of the expression a/csin2C+c/asin2A is 1/2 (b) (sqrt(3))/2 (c) 1 (d) sqrt(3)

Let A B C be a triangle such that /_A C B=pi/6 and let a , ba n dc denote the lengths of the side opposite to A , B ,a n dC respectively. The value(s) of x for which a=x^2+x+1,b=x^2-1,a n dc=2x+1 is(are) -(2+sqrt(3)) (b) 1+sqrt(3) 2+sqrt(3) (d) 4sqrt(3)

If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (a) (c^2)/(sqrt(a b)) (b) (c^3)/(a b) (c) (c^3)/(sqrt(2a b)) (d) (c^3)/(2a b)

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

In acute angled triangle A B C ,A D is the altitude. Circle drawn with A D as its diameter cuts A Ba n dA Ca tPa n dQ , respectively. Length of P Q is equal to /(2R) (b) (a b c)/(4R^2) (c) 2RsinAsinBsinC (d) delta/R