The d.r's of the lines AB and AC are (1,2,-2) and (2,-3,6) the d.r’s of the bisector of `/_BAC` are

The vertices of a triangle are A(5,4,6),B(1,-1,3) and (4,3,2) . The internal bisector of /_BAC meets BC in D. Find AD.

If the d.R.s of two lines are 1,-2,-2 and 2,-2,1 , then the measures of the acute angle between them is

The vertices of a triangle ABC are are A(1,3,5),B(-2,4,7) and C(3,2,2). Then the direction cosines of the vector along bisector of /_BAC is

The d.r.'s of the line AB are (6,-2,9) . If the line AB makes angles alpha,beta with OY, OZ respectively where O=(0,0,0) then sin^(2)alpha-sin^(2)beta= .....

If two chords AB and AB of a circle with centre O are such that the centre O lies on the bisector of /_BAC; Prove that AB=AC

If two chords AB and AC of a circle with centre O are such that the centre O lies on the bisector of /_BAC, prove that AB=AC, i.e. the chords are equal.

A(-1,2,-3),B(5,0,-6) and C(0,4,-7) are the vertices of a triangle.The DRs of the internal bisector of /_BAC are

The equations of the perpendicular bisector of the sides AB and perpendicular bisector of the sides AB and AC of a /_ABC are x-y+5=0 and x+2y=0 respectively,if the point Ais (1,-2), then the equation ofthe line BC is

If theta is the angle between two lines whose d.r's are (1,-2,1) and (4,3,2) then sec((theta)/(2))+cosec((theta)/(2)) =

In the given figure,AB and AC are two equal chords of a circle with centre O.Show that o lies on the bisectors of /_BAC.