CAT 2020 Slot 2 QA Question 18: Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the

Question

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the

Accepted Answer

Place $O$ at $(0, 0)$. Then $A = (0, 4)$ and $B = (3, 0)$.

The line through $A$ and $B$ has intercept form
$\dfrac{x}{3} + \dfrac{y}{4} = 1$
$4x + 3y = 12$

The distance from the center $O$ to this chord is
$d = \dfrac{12}{\sqrt{4^2 + 3^2}} = \dfrac{12}{5}$

For a circle of radius 5, chord length i

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to