The equation of circumcircle of an equilateral triangle is $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ and one vertex of the triangle is (1, 1). The equation of incircle of the triangle is:

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

$4 (x^{2} + y^{2}) = g^{2} + f^{2}$

$4 (x^{2} + y^{2}) + 8 g x + 8 f y = (1 - g) (1 + 3 g) + (1 - f) (1 + 3 f)$

$4 (x^{2} + y^{2}) + 8 g x + 8 f y = g^{2} + f^{2}$

$4 (x^{2} + y^{2}) + 8 (g^{2} + f^{2}) = 0$

answer is B.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Incircle and circumcircle have same centre but radius is half of that of circumcircle
Also c = - (2g + 2f + 2) as (1, 1) lies on circumcircle.

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

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

Take Free Test