Question

using vectors prove that the angle in a semicircle is a right angle.

Answer 1

got it till here...

Answer 2

a = x,y
b = c-x, -y

Answer 3

|a| = sqrt(x^2+y^2)
|b| = sqrt((c-x)^2+y^2)

Answer 4

a.b = cx -x^2 - y^2
----- ---------------------- = 0 if cx-x^2-y^2 = 0
|a||b| = sqrt(c^2+x^2 -2cx + y^2)

Answer 5

Thank you! @ amistre64

Answer 6

show that the results of that have to fit a circle equation:

(x-c/2)^2 + y^2 = (c/2)^2