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IIT JEE Advanced 2006 Paper 1

Paragraph for Questions 110–112:

Let ABCD be a square of side length 2 units.

C_2

is the circle through vertices A, B, C, D and

C_1

is the circle touching all the sides of square ABCD. L is the line through A.

Section: Mathematics

Question : 112 of 120

Marks: +1, -0

T_2

T_3

T_1

\Delta T_1T_2T_3

Solution:

The line parallel to BD that passes through point A is

y + 1 = −(x + 1)

y + 1 = −x – 1

⇒ x + y + 2 = 0

AT_1

\frac{OA}{2}

\frac{\sqrt{2}}{2}

\frac{1}{\sqrt{2}}

AT_2

AT_2

2AT_1

\sqrt{2}

The locus of S is a parabola. Therefore, the area of

\Delta T_1T_2T_3

\frac{1}{2} \times \frac{1}{\sqrt{2}} \times 2\sqrt{2}

\frac{1}{2} \times 2

= 1 sq. unit.

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