GATE 2026 BT – Question 53
A straight line $y = x - 1$ intersects a circle with center at $x = 1$, $y = 1$ and radius of magnitude 1 at two points. The length of the chord formed by this intersection is _______. (rounded off to three decimal places)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 1.404 to 1.424
Explanation
The distance from the centre (1, 1) to the line $x - y - 1 = 0$ is $d = \frac{|1 - 1 - 1|}{\sqrt 2} = 0.7071$. The chord length is $2\sqrt{r^2 - d^2} = 2\sqrt{1 - 0.5} = 1.414$.