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Question
Two lines intersect perpendicularly at A and a third line meets the two lines at B and C. A line is drawn from A such that the line is equidistant from the two perpendicularly intersecting lines. If ABC is an isosceles triangle, then the line drawn from A will always pass through
Two lines intersect perpendicularly at A and a third line meets the two lines at B and C. A line is drawn from A such that the line is equidistant from the two perpendicularly intersecting lines. If ABC is an isosceles triangle, then the line drawn from A will always pass through
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Solution
The correct option is A midpoint of BC
The locus of a point equidistant from two lines is the bisector of the angle between the two lines. Using angle bisector theorem, the bisector of an angle in a triangle divides the side opposite to the angle in the ratio of the lengths of the sides containing the angle.Since the given triangle is isosceles, the sides containing the angle are equal and therefore it bisects the opposite side. It passes through the midpoint of BC.
midpoint of BC
The locus of a point equidistant from two lines is the bisector of the angle between the two lines. Using angle bisector theorem, the bisector of an angle in a triangle divides the side opposite to the angle in the ratio of the lengths of the sides containing the angle.Since the given triangle is isosceles, the sides containing the angle are equal and therefore it bisects the opposite side. It passes through the midpoint of BC.
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