If segment AB is a diameter, AB =10, and measure angle ABC =45, how far is segment BC from the center of circle O?
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
In ∆ABC, what is segment BC if segment AB=10?
To find the distance between segment BC and the center of circle O, we can use the properties of a circle and right triangles.
Since segment AB is a diameter, it passes through the center of the circle O. Therefore, the center of the circle is the midpoint of segment AB.
Given AB = 10, we can find the length of segment BC by using the properties of right triangles formed by radii of the circle.
In a right triangle, the hypotenuse (AB) is double the length of the shorter side (BC) when the angle between them is 45 degrees.
Therefore, we can calculate BC as follows:
BC = AB / 2 = 10 / 2 = 5
So segment BC is 5 units away from the center of circle O.