In `triangleABC`, vertex A is (1, 2). If the internal angle bisector of `angle B` is `2x- y+10=0` and the perpendicular bisector of AC is y = x, then find the equation of BC

Let ABC be a triangle and A -= (1,2) ,y = x be the perpendicular bisector of AB and x-2y+1=0 be the perpendicular bisector of angle C . If the equation of BC is given by ax+by-5 = 0 then the value of a -2b is

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

In a triangle ABC , AB = AC and angle A = 36^(@) If the internal bisector of angle C meets AB at D . Prove that AD = BC.

In any triangle ABC, if the angle bisector of /_A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.

ABC is a triangle and the internal angle bisector of angle A cuts the side BC at D. If A=(3,-5), B(-3,3), C=(-1,-2) then find the length AD

Let the equations of side BC and the internal angle bisector of angle B of DeltaABC are 2x-5y+a=0 and y+x=0 respectively. If A=(2, 3) , then the value of of a is equal to

Consider a A B C is which side A Ba n dA C are perpendicular to x-y-4=0a n d2x-y-5=0, respectively. Vertex A is (-2,3) and the circumcenter of A B C is (3/2,5/2)dot The equation of line in column I is of the form a x+b y+c=0 , where a , b , c in Idot Match it with the corresponding value of c in column I I Column I|Column II Equation of the perpendicular bisector of side B A |p. -1 Equation of the perpendicular bisector of side A C |q. 1 Equation of side A C |r. -16 Equation of the median through A |s. -4

In triangle ABC, the coordinates of the vertex A are , (4,-1) and lines x - y - 1 = 0 and 2x - y = 3 are the internal bisectors of angles B and C . Then the radius of the circles of triangle AbC is

Let A,B,C be angles of triangles with vertex A -= (4,-1) and internal angular bisectors of angles B and C be x - 1 = 0 and x - y - 1 = 0 respectively. If A,B,C are angles of triangle at vertices A,B,C respectively then cot ((B)/(2))cot .((C)/(2)) =

Consider a triangle ABC with vertex A(2, -4) . The internal bisectors of the angle B and C are x+y=2 and x- 3y = 6 respectively. Let the two bisectors meet at I .if (a, b) is incentre of the triangle ABC then (a + b) has the value equal to