A circle of radius 1 is inscribed in an equilateral triangle

MATHEMATICS · Single correct · CBSE · Mathematics · Circles · Circles

Problem

A circle CC of radius 1 is inscribed in an equilateral triangle PQRPQR. The points of contact of CC with the sides PQPQ, QRQR, RPRP are DD, EE, FF, respectively. The line PQPQ is given by the equation 3x+y−6=0\sqrt{3}x + y - 6 = 0, and the point DD is (332,32)\left(\frac{3\sqrt{3}}{2}, \frac{3}{2}\right). It is given that the origin and the centre of CC are on the same side of the line PQPQ. Find the equation of circle CC. (1) (x−23)2+(y−1)2=1(x - 2\sqrt{3})^2 + (y - 1)^2 = 1 (2) (x−23)2+(y+12)2=1(x - 2\sqrt{3})^2 + \left(y + \frac{1}{2}\right)^2 = 1 (3) (x−3)2+(y+1)2=1(x - \sqrt{3})^2 + (y + 1)^2 = 1 (4) (x−3)2+(y−1)2=1(x - \sqrt{3})^2 + (y - 1)^2 = 1

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