Formula OF R || r || r1 r2 and r3 with ProOF

ProOF OF formula OF r, r1, r2 and r3

There circle C_1,C_2 and C_3 with radii r_1 , r_2 and r_3 (where r_1 तीन वृत्त C_1,C_2 तथा C_3 जिनको त्रिज्याएँ r_1 , r_2 तथा r_3 है, (जहाँ r_1

Formulae OF inradius(r)||ex-radius(r1,r2,r3)

The possible percentage error in computing the parallel resistance R of three resistances 1/R=(1)/R_1+ 1/R_2 1/R_3 from the formula , if R_1, R_2, R_3 are each in error by plus 1.2% is :

Illustration Based Upon r || r1|| r2 || r3

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_(1) , 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)))

For any three non-zero vectors r_1,r_2 and r_3 .|(r_1.r_1,r_1.r_2,r_1.r_3),(r_2.r_1,r_2.r_2,r_2.r_3),(r_3.r_1,r_3.r_2,r_3.r_3)|=0. Then which of the following is false