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A circle C of radius 1 is inscribed in a...

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 `sqrt3 x+ y -6 = 0` and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. (1)The equation of circle C is (2)Points E and F are given by (3)Equation of the sides QR, RP are

A. `y=(2)/(sqrt3)+x+1,y=-(2)/(sqrt3)x-1`
B. `y=(1)/(sqrt3)x,y=0`
C. `y=(sqrt3)/(2)x+1,y=-(sqrt3)/(2)x-1`
D. `y=sqrt3x,y=0`

A

`(x-2sqrt3)^(2)+(y-1)^(2)=1`

B

`(x-2sqrt3)^(2)+(y+(1)/(2))^(2)=1`

C

`(x-sqrt3)^(2)+(y+1)^(2)=1`

D

`(x-sqrt3)^(2)+(y-1)^(2)=1`

Text Solution

Verified by Experts

The correct Answer is:
D
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