Let C be a circle passing through the points A (2,-1) and B (3,4). The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle ( x -5)2+( y -1)2=(13/2), then r 2 is equal to :

Question

Let C be a circle passing through the points A (2,-1) and B (3,4). The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle ( x -5)2+( y -1)2=(13/2), then r 2 is equal to : (A) 32 (B) (65/2) (C) (61/2) (D) 30

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a042c2f19a59463123f0590dba07a150-.png" /> AB =√26 r 2= CM 2+ AM 2 =(2 × √(13/2))2+(√(13/2))2 r 2=(65/2)

Q. Let $C$ be a circle passing through the points $A (2, - 1)$ and $B (3, 4)$ . The line segment $A B$ is not a diameter of $C$ . If $r$ is the radius of $C$ and its centre lies on the circle $(x - 5)^{2} + (y - 1)^{2} = \frac{13}{2}$ , then $r^{2}$ is equal to :

$32$

$\frac{65}{2}$

$\frac{61}{2}$

$30$

$A B = 26$
$r^{2} = C M^{2} + A M^{2}$
$= (2 \times \frac{13}{2})^{2} + (\frac{13}{2})^{2}$
$r^{2} = \frac{65}{2}$

Q. Let C be a circle passing through the points A(2,−1) and B(3,4). The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle (x−5)2+(y−1)2=213​, then r2 is equal to :

32

265​

261​

30