Let `f, g and h` be the lengths of the perpendiculars from the circumcenter of `Delta ABC` on the sides a, b, and c, respectively. Prove that `(a)/(f) + (b)/(g) + (c)/(h) = (1)/(4) (abc)/(fgh)`

If in Delta ABC , sides a, b, c are in A.P. then

If BM and CN are the perpendiculars drawn on the sides AC and BC of the Delta ABC , prove that the points B, C, M and N are concyclic.

AD, BE and CF are the medians of triangle ABC whose centroid is G. If the points A, F, G and E are concyclic, then prove that 2a^(2) = b^(2) + c^(2)

If in Delta ABC, b = 3 cm, c = 4 cm and the length of the perpendicular from A to the side BC is 2 cm, then how many such triangle are possible ?

In a acute angled triangle ABC, proint D, E and F are the feet of the perpendiculars from A,B and C onto BC, AC and AB, respectively. H is orthocentre. If sinA=3/5a n dB C=39 , then find the length of A H

If g, h, k denotes the side of a pedal triangle, then prove that (g)/(a^(2))+ (h)/(b^(2))+ (k)/(c^(2))=(a^(2)+b^(2) +c^(2))/(2 abc)

D , E , F are the foot of the perpendicular from vertices A , B , C to sides B C ,\ C A ,\ A B respectively, and H is the orthocentre of acute angled triangle A B C ; where a , b , c are the sides of triangle A B C , then H is the incentre of triangle D E F A , B ,\ C are excentres of triangle D E F Perimeter of D E F is a cos A+b cos B+c\ cos C Circumradius of triangle D E F is R/2, where R is circumradius of A B C

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.

In a triangle ABC , the sides a , b , c are in G.P., then the maximum value of angleB is

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: area of BDEF is half the area of Delta ABC.