The circumcenter of a triangle formed by the lines and , is
Explanation for the correct option:
Step 1: Finding the co-ordinates
Given, the equation of lines by which the triangle is formed are: and
Re-writing the given equation of lines, we get
Therefore, or .
Hence, , and are equations of the line.
On solving the equation and , we get .
Therefore, the point of intersection is .
On solving the equation and , we get .
Therefore, the point of intersection is .
On solving the equation and , the point of intersection is .
Hence, the coordinates of triangle are .
Step 2: Finding the circumcenter
Now, these three lines make a right-angled triangle.
So, the circumcenter of the right-angled triangle is at the midpoint of the hypotenuse.
Hence, the midpoint and circumcenter lie on a single point.
The midpoint formula is given by .
Here the endpoints of hypotenuse are .
The circumcentre of the triangle is .
Therefore, option (A) is the correct answer.