Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6

Q.

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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away
An Intiative by Sri Chaitanya

a

4x2+y2+8gx+8fy=g2+f2

b

4x2+y2=g2+f2

c

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

d

none of these

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

detailed_solution_thumbnail

In an equilateral triangle, circumcenter and incenter are coincident. 

Therefore, Incenter (g,f)

  Since  Point (1,1) lies on the circle. 

12+12+2g+2f+c=0 or  c=2(g+f+1)

  Also, in an equilateral triangle,

 Circumradius =2× Inradius   Inradius =12×g2+f2c

Therefore, the eqlration of the incircle is (x+g)2+(y+f)2=14g2+f2c =14g2+f2+2(g+f+1)4x2+y2+8gx+8fy=1-g1+3g+1-f1+3f

Watch 3-min video & get full concept clarity

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

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