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`

ABC is a right angled triangle , right angled at C and P is the length of perpendicular from C on AB. If a, b and C are the length of sides BC, CA and AB respectively. Then___

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

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 HD.HE.HF is

Delta ABC is an acute angle triangle inscribed in a circle in a circle .AD is a diameter of the circle . Two perpendiculars BE and CF are drawn from B and C to AC and AB respectively , which intersect each other at the point G . Prove that BDCG is a parallelogram.

In DeltaABC , AB = AC. The perpendiculars drawn from B and C to AC and AB respectively, intersect the sides AC and AB at the points E and F respectively. Prove that FE||BC.

Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a n dF be the feet of the perpendiculars from I to the sides B C ,C A ,a n dA B , respectively. If r_1,r_2a n dr_3 are the radii of circles inscribed in the quadrilaterals A F I E ,B D I F ,a n dC E I D , respectively, prove that (r_1)/(r-1_1)+(r_2)/(r-r_2)+(r_3)/(r-r_3)=(r_1r_2r_3)/((r-r_1)(r-r_2)(r-r_3))

Circumradius of DeltaABC is 3 cm and its area is 6 cm^(2) . If DEF is the triangle formed by feet of the perpendicular drawn from A,B and C on the sides BC, CA and AB, respectively, then the perimeter of DeltaDEF (in cm) is _____

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

In the triangle ABC, if a=5, b=7 and c=3, find the angle B and the circumradius R.