Triangles

A triangle can have:

Let A(3, 0, - 1) , B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the mid-point of AC. If G divides BM in the ratio 2:1, then cos( ∠GOA ) (O being the origin) is equal to______.

A triangle with vertices (4, 0), (-1,-1), (3, 5) is

Match List-I and List-II

LIST I		LIST II
A.	No. of triangles formed using 5 points in a line and 3 points on parallel line is	I.	20
B.	No. of diagonals drawn using the vertices of an octagon	II.	10
C.	The no. of diagonals in a regular polygon of 100 sides is	III.	45
D.	A polygon with 35 diagonals has sides	IV.	4850

Choose the correct answer from the options given below:

Which of the following is true:
A. If a cos A = b cos B, then the triangle is isosceles or right angled.
B. If in a triangle ABC, cos A cos B + sin A sin B sin C =1 then the triangle is isosceles right angled.
C. If the ex-radii r1, r2, r3 of ΔABC are in the HP, then it's sides are not in AP
Choose the correct answer from the options given below :