Thread: geometric and quadratic equations

The line x + y - 1 = 0 intersects the circle x^2 + y^2 = 13 at A(x1,y1) and B(x2, y2). Without finding the coordinates of A and B, find the length of the chord AB.

HINT: form a quadratic equation in x and evaluate l x1 - x2 l and l y1 - y2 l

thanks

how do i got about doing this question

If you solve these equations simultaneously you get and , so

and and so

Now using Pythagorus' Theorem you have

So the length of the chord is units