+681 A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 1, and the line is y = x.
+1297
A line and a circle intersect at A and B as shown below. Find the distance between and A and B.
The circle is x^2 + y^2 = 1, and the line is y = x.
x2 + y2 = 1 is a circle, centered on the origin, and radius 1.
y = x is a straight line, that passes through the origin.
Since the straight line passes through the center of the circle,
it creates a diameter through the intersection points A and B.
The radius of the circle is 1, so its diameter is twice that.
So, the distance between A & B, i.e., the diameter, is 2.
.
+1297
A line and a circle intersect at A and B as shown below. Find the distance between and A and B.
The circle is x^2 + y^2 = 1, and the line is y = x.
x2 + y2 = 1 is a circle, centered on the origin, and radius 1.
y = x is a straight line, that passes through the origin.
Since the straight line passes through the center of the circle,
it creates a diameter through the intersection points A and B.
The radius of the circle is 1, so its diameter is twice that.
So, the distance between A & B, i.e., the diameter, is 2.
.
