Let ABC be a triangle with incentre I. If P and Q are the feet of the perpendiculars from A to BI and CI, respectively, then prove that `(AP)/(BI) + (AQ)/(Cl) = cot.(A)/(2)`

Let ABC be a triangle with incentre at I. Also, let P and Q be the feet of perpendiculars from A to BI and CI, respectively. Then which of the following result are correct?

Let A B C be a triangle with incentre at I Also, let P and Q be the feet of perpendiculars from A to BI and CI respectively. Then which of the following results are correct? (A P)/(B I)=(sinB/2cosC/2)/(sinA/2) (b) (A Q)/(C I)=(sinC/2cosB/2)/(sinA/2) (A P)/(B I)=(sinC/2cosB/2)/(sinA/2) (d) (A P)/(B I)+(A Q)/(C I)=sqrt(3)if/_A=60^0

Let A B C be a triangle with incentre at I Also, let P and Q be the feet of perpendiculars from A to BI and CI respectively. Then which of the following results are correct? (A P)/(B I)=(sinB/2cosC/2)/(sinA/2) (b) (A Q)/(C I)=(sinC/2cosB/2)/(sinA/2) (A P)/(B I)=(sinC/2cosB/2)/(sinA/2) (d) (A P)/(B I)+(A Q)/(C I)=sqrt(3)if/_A=60^0

Let A B C be a triangle with incentre at Idot Also, let Pa n dQ be the feet of perpendiculars from AtoB Ia n dC I , respectively. Then which of the following results are correct? (A P)/(B I)=(sinB/2cosC/2)/(sinA/2) (b) (A Q)/(C I)=(sinC/2cosB/2)/(sinA/2) (A P)/(B I)=(sinC/2cosB/2)/(sinA/2) (d) (A P)/(B I)+(a Q)/(C I)=sqrt(3)if/_A=60^0

Let ABC be a triangle with incentre I and inradius r. Let D, E, F be the feet of the perpendiculars from I to the sides BC, CA and AB, respectively, If r_(2)" and "r_(3) are the radii of circles inscribed in the quadrilaterls AFIE, BDIF and CEID respectively, then prove that r_(1)/(r-r_(1))+r_(2)/(r-r_(2))+r_(3)/(r-r_(3))=(r_(1)r_(2)r_(3))/((r-r_(1))(r-r_(2))(r-r_(3)))

Let ABC be a triangle with incentre I and inradius r. Let D, E, F be the feet of the perpendiculars from I to the sides BC, CA and AB, respectively, If r_(2)" and "r_(3) are the radii of circles inscribed in the quadrilaterls AFIE, BDIF and CEID respectively, then prove that r_(1)/(r-r_(1))+r_(2)/(r-r_(2))+r_(3)/(r-r_(3))=(r_(1)r_(2)r_(3))/((r-r_(1))(r-r_(2))(r-r_(3)))

An isosceles triangle ABC is right angled at B.D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of Delta ABC . If AP = a cm, AQ = b cm and angle BAD= 15^(@), sin 75^(@)=

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 rarr BC,CA and AB, respectively. The value of (IDxIExIF)/(IAxIBxIC) is equal to (a) (5)/(2) (b) (5)/(4)(c)10(d)(1)/(5)

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 _____

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 _____