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Question: If a circle of radius r is touching the lines x<sup>2</sup> – 4xy + y<sup>2</sup> = 0 in the first q...

If a circle of radius r is touching the lines x2 – 4xy + y2 = 0 in the first quadrant at point A & B, then area of DOAB (O being origin) is –

A

33\sqrt{3}r2

B

33r24\frac{3\sqrt{3}r^{2}}{4}

C

3r24\frac{3r^{2}}{4}

D

r2

Answer

33r24\frac{3\sqrt{3}r^{2}}{4}

Explanation

Solution

Find tan 2q = 24−12\frac{2\sqrt{4 - 1}}{2}

q = 300

Area of D AOB = 12\frac{1}{2} (OA. OB) sin 600

= 12\frac{1}{2} (r cot q)2.32\frac{\sqrt{3}}{2}