Show that the perpendicular from the vertices of a triangle to the opposites sides are concurrent .

Prove analytically that in any triangle the perpendiculars drawn from the vertices upon the opposite sides are concurrent.

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

If x,y,z are the perpendiculars from the vertices of a triangle ABC on the opposite sides a,b,c respectively, then show that (bx)/c+(cy)/a+(az)/b=(a^2+b^2+c^2)/(2R)

The perpendicular from the vertices A, B and C of a triangle ABC on the opposite sides meet at O. If OA=x, OB=y and OC=z, prove that, a/x + b/y + c/z = (abc)/(xyz) .

By vector method show that , the perpendicular bsectors of the sides of a triangle are concurrent .

The three angular points of a triangle are given by Z=alpha, Z=beta,Z=gamma,w h e r ealpha,beta,gamma are complex numbers, then prove that the perpendicular from the angular point Z=alpha to the opposite side is given by the equation R e((Z-alpha)/(beta-gamma))=0

Let the lengths of the altitudes drawn from the vertices of Delta ABC to the opposite sides are 2, 2 and 3. If the area of Delta ABC " is " Delta , then find the area of triangle

Prove that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

Prove analytically that the perpendicular bisector of the sides of a triangle ar concurrent.

In DeltaABC, P,Q, R are the feet of angle bisectors from the vertices to their opposite sides as shown in the figure. DeltaPQR is constructed If angleBAC = 120^(@) , then measusred of angleRPQ will be