1. ## 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

2. If you solve these equations simultaneously you get $x_1=-2$ and $x_2=3$ , so $\left |x_1-x_2\right |=5$

and $y_1=3$ and $y_2=-2$ so $\left |y_1-y_2\right |=5$

Now using Pythagorus' Theorem you have $C=\sqrt{5^2+5^2}$

So the length of the chord is $5\sqrt{10}$ units