The line y = 3x - 10 intersects a circle centered at the origin at A and B. We know the lenght of chord AB is \(18\). Find the area of the circle.
+128406 We can find the distance from the origin to the line as
l 3(0) - 1(0) - 10 l / sqrt ( 3^2 + 1^2) = 10 / sqrt 10 = sqrt 10
Half the length of the chord = 9
We can form a right triangle with legs of sqrt 10 and 9 and hypotenuse, r
The radius^2 of the circle is 10 + 81 = 91
So....the area = pi * r^2 = 91 pi ≈ 285.9
