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`

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC . Given AH.BH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of R is

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC . Given AH.BH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of (cos A. cos B . cos C)/(cos^(2)A + cos^(2)B + cos^(2)C) is

In an acute angled triangle ABC, angleA=20^(@) , let DEF be the feet of altitudes through A, B, C respectively and H is the orthocentre of DeltaABC . Find (AH)/(AD)+(BH)/(BE)+(CH)/(CF) .

In an acute angled triangle ABC, angleA=20^(@) , let DEF be the feet of altitudes through A, B, C respectively and H is the orthocentre of DeltaABC . Find (AH)/(AD)+(BH)/(BE)+(CH)/(CF) .

For a triangle ABC, R = (5)/(2) and r = 1 . Let D, E and F be the feet of the perpendiculars from incentre I to BC, CA and AB, respectively. Then the value of ((IA) (IB)(IC))/((ID)(IE)(IF)) is equal to _____

Delta ABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.

In a triangle A B C , the angles at B and C are acute. If BE and CF be drawn perpendiculars on AC and AB respectively, prove that B C^2=A B*B F+A C*C Edot

In an acute angle Delta ABC, let AD, BE and CF be the perpendicular from A, B and C upon the opposite sides of the triangle. (All symbols used have usual meaning in a tiangle.) The orthocentre of the Delta ABC, is the

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

For triangle ABC,R=5/2 and r=1. Let I be the incenter of the triangle and D,E and F be the feet of the perpendiculars from I->BC,CA and AB, respectively. The value of (ID*IE*IF)/(IA*IB*IC) is equal to (a) 5/2 (b) 5/4 (c) 1/10 (d) 1/5