Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

If DeltaABC is an isosceles triangle with AB = AC. Prove that the perpendiculars from the vertices B and C to their opposite sides are equal.

If A B C is an isosceles triangle with A B=A C . Prove that the perpendiculars from the vertices B and C to their opposite sides are equal.

If A B C is an isosceles triangle with A B=A Cdot Prove that the perpendiculars from the vertices B\ a n d\ C to their opposite sides are equal.

Altitudes the perpendiculars drawn from the vertices of a triangle to the opposite side are known as the altitudes of the triangle.

Consider a triangle ABC, where c,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters R,r S,Delta denote the circumradius, inradius semi-perimeter and area of the triangle respectively. If (bx)/(c) +(cy)/(a)+(az)/(b) =(a^(2) +b^(2)+c ^(2))/(k), then the value of k is

Consider a triangle ABC, where c,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters R,r S,Delta denote the circumradius, inradius semi-perimeter and area of the triangle respectively. If cot A+cot B+ cot C= k ((1)/(x^(2))+ (1)/(y^(2))+(1)/(z^(2))), then the value of k is

Consider a triangle ABC, where c,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters R,r S,Delta denote the circumradius, inradius semi-perimeter and area of the triangle respectively. The valur of (c sin B+b sin C)/(x)+ (a sin C +c sin A)/(y)+(b sin A+a sin B)/(z) is equal to

If p_(1), p _(2), p_(3) are respectively the perpendicular from the vertices of a triangle to the opposite sides, then find the value of p_(1) p_(2)p _(3).

If p_(1),p_(2),p_(3) are the perpendiculars from the vertices of a triangle to the opposite sides, then prove that p_(1)p_(2)p_(3)=(a^(2)b^(2)c^(2))/(8R^(3))

If p_(1), p_(2),p_(3) are respectively the perpendiculars from the vertices of a triangle to the opposite sides , then (cosA)/(p_(1))+(cosB)/(p_(2))+(cosC)/(p_(3)) is equal to