Question

The length of the chord of the circle $(x-3{)}^2+(y-5{)}^2=80$ cut off by the line $3x-4y-9=0$ is

• A. $16$
• B. $8$
• C. $\sqrt{96}$
• D. $2\sqrt{96}$

Answer 1

Answer: (A)

$16$

$(x-3{)}^2+(y-5{)}^2=80$

cut off by the line $3x-4y-9=0$

$OP=\left|\frac{9-20-9}{5}\right|$

$OP=4cm$

$PA=\sqrt{\left(80\right)-\left(16\right)}$

$PA=\sqrt{64}=8$

$AB=16cm$