The equation of circumcircle of an equilateral triangle is x2+y2+2gx+2fy+c=0 and one vertex of the triangle is (1,1).The equation of incircle of the triangle is

a.4(x²+y²)=g²+f²

b.4(x²+y²)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f)

c.4(x²+y²)+8gx+8fy=g²+f²

d.none of these

Question

The equation of circumcircle of an equilateral triangle is x2+y2+2gx+2fy+c=0 and one vertex of the triangle is (1,1).The equation of incircle of the triangle is

a.4(x²+y²)=g²+f²

b.4(x²+y²)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f)

c.4(x²+y²)+8gx+8fy=g²+f²

d.none of these

Ashwin Muralidharan IIT Madras · Answer

Hi Menka,

Note that the distance between Centre (-g,-f) nad the Vertex (1,1) = R

In equilateral Triangle r=R/2

So Eqn of incircle is (x+g)^2 + (y+f)^2 = r^2 = (R^2)/4 = 1/4 [ (g+1)^2 + (f+1)^2 ]

Simplify this eqn. It is option (B).

Best Regards,

Ashwin (IIT Madras).

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The equation of circumcircle of an equilateral triangle is x2+y2+2gx+2fy+c=0 and one vertex of the triangle is (1,1).The equation of incircle of the triangle is a.4(x 2 +y 2 )=g 2 +f 2 b.4(x 2 +y 2 )+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f) c.4(x 2 +y 2 )+8gx+8fy=g 2 +f 2 d.none of these

The equation of circumcircle of an equilateral triangle is x2+y2+2gx+2fy+c=0 and one vertex of the triangle is (1,1).The equation of incircle of the triangle is

a.4(x²+y²)=g²+f²

b.4(x²+y²)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f)

c.4(x²+y²)+8gx+8fy=g²+f²

d.none of these

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The equation of circumcircle of an equilateral triangle is x2+y2+2gx+2fy+c=0 and one vertex of the triangle is (1,1).The equation of incircle of the triangle is a.4(x 2 +y 2 )=g 2 +f 2 b.4(x 2 +y 2 )+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f) c.4(x 2 +y 2 )+8gx+8fy=g 2 +f 2 d.none of these

The equation of circumcircle of an equilateral triangle is x2+y2+2gx+2fy+c=0 and one vertex of the triangle is (1,1).The equation of incircle of the triangle is a.4(x2+y2)=g2+f2 b.4(x2+y2)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f) c.4(x2+y2)+8gx+8fy=g2+f2 d.none of these

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The equation of circumcircle of an equilateral triangle is x2+y2+2gx+2fy+c=0 and one vertex of the triangle is (1,1).The equation of incircle of the triangle is

a.4(x²+y²)=g²+f²

b.4(x²+y²)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f)

c.4(x²+y²)+8gx+8fy=g²+f²

d.none of these