Home
Class 11
MATHS
On the Argand plane z1, z2a n dz3 are re...

On the Argand plane `z_1, z_2a n dz_3` are respectively, the vertices of an isosceles triangle `A B C` with `A C=B C` and equal angles are `thetadot` If `z_4` is the incenter of the triangle, then prove that `(z_2-z_1)(z_3-z_1)=(1+sectheta)(z_4-z_1)^2dot`

Promotional Banner

Similar Questions

Explore conceptually related problems

If z_(1),z_(2) and z_(3) are the vertices of a right angledtriangle in Argand plane such that |z_(1)-z_(2)|=3,|z_(1)-z_(3)|=5 and z_(2) is the vertex with the right angle then

If z_(1),z_(2),z_(3) are the vertices of an isosceles triangle right angled at z_(2), then prove that (z_(1))^(2)+2(z_(2))^(2)+(z_(3))^(2)=

Let vertices of an acute-angled triangle are A(z_(1)),B(z_(2)), and C(z_(3))* If the origin O is he orthocentre of the triangle,then prove that z_(1)(bar(z))_(2)+(bar(z))_(1)z_(2)=z_(2)(bar(z))_(3)+(bar(z))_(2)z_(3)=z_(3)(bar(z))_(1)+(bar(z))_(3)z_(1)

If z_(1),z_(2),z_(3) are the vertices of an equilateral triangle,then value of (z_(2)-z_(3))^(2)+(z_(3)-z_(1))^(2)+(z_(1)-z_(2))^(2)

If the points A(z),B(-z) and C(z+1) are vertices of an equilateral triangle then

If the points z_(1),z_(2),z_(3) are the vertices of an equilateral triangle in the Argand plane, then which one of the following is not correct?