Given a triangle ABC with sides a = 5, b = 6, c = 3. Let M, K be respectively two points of segments AB, BC such that BM = 1, BK = 2. a) Compute angles A, B, C. b) Compute MK and the area of triangle BMK

1) Given a triangle ABC with sides a=5, b=6, c=3. Let M, K be respectively two points of segments AB, BC such that BM=1, BK=2.
a) Compute angles A, B, C
b) Compute MK and the area of triangle BMK
c) Let I be midpoint of MK. Caculate the length of the median from vertex B of triangle BMK.

2) Given triangle ABC. Prove that:
a) If b(b2-a2) = c(a2-c2) then A=60*
b) If a=2b x cosC then triangle ABC is isosceles at A
c) If S=2 x R2 x sinB x sinC then triangle ABC is right triangle at A.