If segment AB is a diameter, AB =10, and measure angle ABC =45, how far is segment BC from the center of circle O?

Answer 1

The line from BC to the centre forms an isosceles right-angled triangle with hypotenuse of 5
if that perpendicular distance is x

x^2 + x^2 = 5^2
x^2 = 25/2
x = 5/√2 or 5√2/2

Answer 2

In ∆ABC, what is segment BC if segment AB=10?