JEE MainMathematicsStraight Lines
The angle bisectors of the lines 7x - y - 10 = 0 and x - y + 2 = 0 intersect a third line 13x - 17y + 50 = 0 to form a triangle. The square of the distance of the orthocenter of this triangle from the origin is
Correct answer
20
Step-by-step solution
The angle bisectors of any two intersecting lines are always perpendicular to each other. Therefore, the triangle formed by the two angle bisectors and the third line 13x - 17y + 50 = 0 is a right-angled triangle, where the right angle is at the point of intersection of the two bisectors. In a right-angled triangle, the orthocenter is exactly the vertex where the right angle is located. The intersection point of the two angle bisectors is the same as the intersection point of the original two lines. Let us solve th