Paragraph: A circle C of radius 1 is inscribed in an equilateral △ PQR . The points of contact of C with the sides PQ , QR , RP are D , E , F respectively. The line PQ is given by the equation 3 x +

Question

Paragraph: A circle C of radius 1 is inscribed in an equilateral △ PQR . The points of contact of C with the sides PQ , QR , RP are D , E , F respectively. The line PQ is given by the equation 3 ​ x + y − 6 = 0 and the point D is ( 2 3 3 ​ ​ , 2 3 ​ ) . Further, it is given that the origin and the centre of C are on the same side of the line PQ . Question: Points E and F are given by

TestHub · Accepted Answer

Slope of line joining centre of circle to point $D$ $= \frac{\frac{3}{2} - 1}{\frac{3 3}{2} - 3} = \frac{1}{3}$ [makes an angle $3 0^{\circ}$ with $X$ -axis] $∴$ Points $E$ and $F$ will make angle $15 0^{\circ}$ and $- 9 0^{\circ}$ with $X$ -axis.
$∴ E$ and $F$ are given by and $∴$ $\frac{x - 3}{cos 15 0 ^{\circ}} \frac{x - 3}{cos ( - 9 0 ^{\circ} )} E an d F = \frac{y - 1}{sin 15 0 ^{\circ}} = 1 = \frac{y - 1}{sin ( - 9 0 ^{\circ} )} = 1 = (\frac{3}{2}, \frac{3}{2}) = (3, 0)$

Mathematics - Straight Lines Question with Solution | TestHub

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