Question

Let AB be the chord $4x-3y+5=0$ of the circle $x^2+y^2-2x+4y-20=0$. If $C=(7,1)$ then the area of triangle ABC is?

• A. $15$ sq. unit.
• B. $20$ sq. unit
• C. $24$ sq. unit
• D. $45$ sq. unit

Answer 1

The correct option is C $24$ sq. unit

REF.Image.

$x^2+y^2-2x+4y-20=0$

centre $\to (1-2)$

radius $\to \left(5\right)$

$ar\left(ABC\right)=\frac{1}{2}\times AB\times (\perp$ ar distance of C from 4x-3y+5 = 0)

$=\left|\frac{4\left(7\right)-3\left(1\right)+5}{5}\right|$

$=6$

$OD=\left|\frac{4\left(1\right)-3\left(2\right)+5}{5}\right|$

$=3$

So $BD=\sqrt{5^2-3^2}=4$

& $AB=4\times 2$ (Property of circles) ($\perp$ ar from

centre bisects the chord)

$ar\left(ABC\right)=\frac{1}{2}\times 8\times 6$

$=24squnits.$