Question

Line \(l:x+y = 4\) intersects the circle \(x^2+y^2-2x-2y = 2\) at points \(A\) and \(B\). If C is the center of the circle, then the area of \(△ABC\) is...

• A. \(\sqrt{2}\)
• B. \(2\)
• C. \(2\sqrt{2}\)
• D. \(4\)

Hint:

Find the centre and radius, then the perpendicular distance from the centre to the line.

Answer 1

The Correct Option is B

Step 1: Check with sides
Triangle ABC has sides $CA = CB = 2$ and $AB = 2\sqrt2$.

Step 2: Right angle
$CA^2+CB^2 = 8 = AB^2$, so angle ACB is a right angle.

Step 3: Area
$\frac12\times2\times2 = 2$. Option (B).

Final Answer:
2. \[ \boxed{\text{(B)}\ 2} \]