Show, by vector methods, that the angularbisectors of a triangle are concurrent and find an expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.

Prove by vector method that the perpendiculars (altitudes) from the vertices to the sides of a triangle are concurrent.

The meeting point of the angle bisectors of a triangle is ___________.

Show that the angles of an equilateral triangle are 60^@ each.

Show that the bisectors of angles of a parallelogram form a rectangle.

If acosA=bcosBthen show that the triangle is either an isosceles triangle or right angled triangle.

Construct the bisector of a given angle ABC.

Show that the given points form a right angled triangle and check whether they satisfies pythagoras theorem. A(1, -4), B(2, -3) and C(4, -7)

The product of the sines of the angles of a triangle is p and the product of their cosines is qdot Show that the tangents of the angles are the roots of the equation q x^3-p x^2+(1+q)x-p=0.

State and prove angle bisector theorem.