The line y = 3x - 10 intersects a circle centered at the origin at A and B. We know the length of chord AB is \(10\). Find the area of the circle.
+128474 If we draw a radius bisecting this chord it will do so at right angles
The distance from the origin to this line is given by
l 3(0) - 1(0) - 10 l / [sqrt 3^2 + 1^2 ] = 10 / sqrt 10 = sqrt 10
So we can form a right triangle with ...... r = the hypotenuse and legs of 5 and sqrt (10)
r^2 = 5^2 + (sqrt 10)^2 = 25 + 10 = 35
Area of the circle = pi * r^2 = pi * 35 = 35 pi units^2
