Recent content by frusciante

Thank you for your response, Evgeny. Indeed that first expression (=1) must hold, but I am having a hard time to prove that $$\frac{ZP}{h_c}+\frac{ZQ}{h_a}+\frac{ZR}{h_b}=1$$ since the two "types" of distances (ZP - h_c etc) aren't parallel given that the triangle is not equilateral. Any idea?

I am struggling with this question, it would be easy enough if the triangle was equilateral but that is not necessarily the case. Let (ha, hb, hc) be heights in the triangle ABC, and let Z be a point inside the triangle. Further to this, consider the points P, Q, R on the sides AB, BC and AC...

Currently revising for my A-Level maths (UK), there is unfortunately no key in the book; Given the triangle with sides a,b,c respectively and the area S, show that ab+bc+ca => 4*sqrt(3)*S I have tried using the Ravi transformation without luck, any takers?