Question

Which of the following statements is/are correct?

1. The radical axis of two circles is the locus of points whose power with respect to the two circles is equal.

2. The common point of intersection of the radical axes of three circles taken two at a time called the radical center of three circles.

• A. Only 1
• B. Only 2
• C. Both 1 and 2
• D. None of these

Answer 1

The correct option is C

Both 1 and 2

Statement 1 is a definition of radical axis.

The radical axis of two circles is the locus of points whose powers with respect to the two circles are equal. The equation of radical axis of the two circles $S_1=0$

$\&S_2=0$ is given by

$S_1-S_2=0$

i.e., $2(g_1-g_2)x+2(f_1-f_2)y+(c_1-c_2)=0$

Statement 2: It is also a definition of radical center. The common point of intersection of the radical axis of three circles taken two at a time is called the radical center of three circles Length of tangents from radical center of the three circles are equal.