Let the tangents drawn from the origin to the circle, x2 + y2- 8x - 4 y + 16 = 0 touch it at the points A and B. The (AB)2 is equal to :

Question

Let the tangents drawn from the origin to the circle, x2 + y2- 8x - 4 y + 16 = 0 touch it at the points A and B. The (AB)2 is equal to : (A) (32/5) (B) (64/5) (C) (52/5) (D) (56/5)

Tardigrade Admin · Accepted Answer

R=√16+4-16=2 L=√S1=4 AB(Chord of contact)=(2LR/√L2+R2)=(8/√5) (AB)2=(64/5)

Q. Let the tangents drawn from the origin to the circle, $x^{2} + y^{2} - 8 x - 4 y + 16 = 0$ touch it at the points A and B. The $(A B)^{2}$ is equal to :

$\frac{32}{5}$

$\frac{64}{5}$

$\frac{52}{5}$

$\frac{56}{5}$

$R = 16 + 4 - 16 = 2$
$L = S_{1} = 4$
$A B$ (Chord of contact) $= \frac{2 L R}{L ^{2} + R ^{2}} = \frac{8}{5}$
$(A B)^{2} = \frac{64}{5}$

Q. Let the tangents drawn from the origin to the circle, x2+y2−8x−4y+16=0 touch it at the points A and B. The (AB)2 is equal to :

532​

564​

552​

556​