Home
Class 12
MATHS
If A(x1, y1), B (x2, y2) and C (x3, y3) ...

If `A(x_1, y_1), B (x_2, y_2) and C (x_3, y_3)` are the vertices of a `DeltaABC and (x, y)` be a point on the internal bisector of angle `A`, then prove that : `b|(x,y,1),(x_1, y_1, 1), (x_2, y_2, 1)|+c|(x, y,1), (x_1, y_1, 1), (x_3, y_3, 1)|=0` where `AC = b and AB=c`.

Promotional Banner

Similar Questions

Explore conceptually related problems

If A(x_(1),y_(1)),B(x_(2),y_(2)) and C(x_(3),y_(3)) are the vertices of a triangle then excentre with respect to B is

If A (x_(1), y_(1)), B (x_(2), y_(2)) and C (x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2)| is equal to

If A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) are the vertices of the triangle then show that:'

If A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4

A(x_(1),y_(1))B(x_(2),y_(2)) and C(x_(3),y_(3)) are the vertices and a,b and c are the sides BC,CA and AB of the triangle ABC respectively then the Coordinates of in centre are I=

A(x_(1),y_(1)) , B(x_(2),y_(2)) , C(x_(3),y_(3)) are the vertices of a triangle then the equation |[x,y,1],[x_(1),y_(1),1],[x_(2),y_(2),1]| + |[x,y,1],[x_(1),y_(1),1],[x_(3),y_(3),1]| =0 represents

If the co-ordinates of the vertices of an equilateral triangle with sides of length a are (x_1,y_1), (x_2, y_2), (x_3, y_3), then |[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]|=(3a^4)/4

If A(3x_(1),3y_(1)),B(3x_(2),3y_(2)),C(3x_(3),3y_(3)) are vertices of a triangle with orthocentre H at (x_(1)+x_(2)+x_(3),y_(1)+y_(2)+y_(3)) then the /_ABC=

A (3,4 ), B (-3, 0) and C (7, -4) are the vertices of a triangle. Show that the line joining the mid-points D (x_1, y_1), E (x_2, y_2) and F (x, y) are collinear. Prove that (x-x_1) (y_2 - y_1) = (x_2 - x_1) (y-y_1)