Paragraph of Question Nos. 15 to 17 A circle C of radius 1 is inscribed in an equilateral triangle 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 √3x + y − 6 = 0 and the point D is ( 3√3 2 , 3 2 ). Further, it is given that the origin and the center of C are on the same side of the line PQ. 1. 15. The equation of circle C is   (x − 2√3)2 + (y − 1)2 = 1   (x − 2√3)2 + (y + 1/2)2 = 1   (x − √3)2 + (y + 1)2 = 1   (x − √3)2 + (y − 1)2 = 1   Hint Half-n-half Clue   2. 16. Points E and F are given by   ( 3 2 , √3 2 ), ( √3 2 , 1 2 )   ( √3 2 , 1 2 ), (√3 , 0)   ( √3 2 , 3 2 ), (√3 , 0)   ( √3 2 , 3 2 ), ( √3 2 , 1 2 )   Half-n-half Clue   3. 17. Equations of the sides QR, RP are   y = 2 √3 x + 1 , y = − 2 √3 x − 1   y = 1 √3 x , y = 0   y = √3 2 x + 1 , y = − √3 2 x − 1   y = √3 x, y = 0   Half-n-half Clue