Grade 11Algebra
Let ABC be a triangle with indenter 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 r1, r2 and r3 are the radii of circles inscribed in the quadrilaterals AFIE, BDIF and CEID respectively, prove thatr1/r – r1 + r2/r - r2 + r3/r – r3 = r1 r2 r3/(r – r1) (r – r2) (r – r3).
Let ABC be a triangle with indenter 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 r1, r2 and r3 are the radii of circles inscribed in the quadrilaterals AFIE, BDIF and CEID respectively, prove that
r1/r – r1 + r2/r - r2 + r3/r – r3 = r1 r2 r3/(r – r1) (r – r2) (r – r3).
