Let ABC be a triangle with no right angle, E on the line BC such that ∠AEB=∠BAC and ΔA the perpendicular to BC at E. Let the circle γ with diameter BC intersect BA again at D. For each point M on γ (M is distinct from B), the line BM meets ΔA at M′ and the line AM meets γ again at M′′.
(a) Show that p(A)=AM′×DM′′ is independent of the chosen M.
(b) Keeping B,C fixed, and let A vary. Show that d(A,ΔA)p(A) is independent of A.Michel Bataille fixedequal anglescirclegeometry