Three straight lines , and
are concurrent with one line bisecting the angle between the other two
Explanation for the correct answer:
Consider the equations of three straight lines
Step 1: Prove that the lines are intersecting
As we can observe, that the slopes of all three lines are unequal (their coefficients of are different). Hence, the lines must be intersecting
Solve equations and simultaneously to obtain the point of intersection
Substitute this value of in we get,
Hence is the point of intersection of lines and
Step 2: Prove that the lines are concurrent
Now substitute these values of in we get,
Hence, point satisfies the equation of line
Hence, the lines are concurrent.
Step 3: Use the formula for angle bisectors of a pair of lines
Angle bisectors of the lines and are given as
Now, the angle bisectors of the lines and is given as
and
and
and
and
is the equation of line
Hence, the lines are concurrent and one line is the angle bisector of the other two.
Hence, option (C) is the correct answer.