The line y = (3x + 7)/2 intersects the circle x^2 + y^2 = 25 at A and B. Find the length of chord AB.
A non-graphical method
The center of the circle = (0,0)
The equation of the line in standard form is
2y = 3x + 7
3x - 2y + 7 = 0 using (0,0) for (x,y).....the distance from the circle's center to the line is given by
l 3(0) - 2(0) + 7 l 7
_________________ = _________ (1)
sqrt [ 3^2 + 2^2] sqrt (13)
We can form a right triangle with a hypotenuse of 5, one leg = (1) and the other leg 1/2 the chord length
So......the length of the whole chord is
2sqrt [ 5^2 - (7/sqrt(13))^2 ] =
2sqrt [ 25 - 49/13 ] =
2sqrt [ 276/13 ] ≈ 9.215 = 9.22 (rounded to the nearest hundreth )