A, B এবং C একটি বৃত্তের তিনটি বিন্দু। প্রমাণ কর যে AB, BC এবং CA এর লম্ব বিভাজক...

Let ABC and A'B'C' be two triangles in which AB gt A'B', BC gt B'C' and CA gt C'A' . Let D, E and F be the midpoints of the sides BC, CA and AB respectively. Let D', E' and F' be the midpoints of the sides B'C', C'A' and A'B' respectively. Consider the following statements : Statement I: AD gt A'D', BE gt B'E' and CF gt C'F' are always true. Statement II : (AB^(2)+BC^(2)+CA^(2))/(AD^(2)+BE^(2)+CF^(2)) =(A'B'^(2)+B'C'^(2)+C'A'^(2))/(A'D'^(2) +B'E'^(2) +C'F'^(2)) Which one of the following is correct in respect of the above statements?

In Fig, 2.38, (a) is CA+CB=AB ? (b) is BA+AC=CB ? (c ) is AB+BC=CA ?

Let s denotes the semi-perimeter of a DeltaABC in which BC=a, CA=b and AB=c. If a circle touches the sides BC, CA, AB, at D, E, F, respectively. Prove that BD=s-b.

If a,b,c are the lengths of sides,BC,CA and AB of a triangle ABC, prove that vec BC+vec CA+vec AB=vec O and deduce that (a)/(sin A)=(b)/(sin B)=(c)/(sin C) .

Suppose a, b, c in C, and |a| = |b| = |c| = 1 and abc = a + b + c , then |bc + ca + ab| is equal to