Statement $-I$: Two lines which pass through a given fixed point and are equally inclined to two other lines passing through the same point,are always perpendicular to each other.
Statement $-II$: Angle bisectors of two intersecting lines are always perpendicular to each other.
Statement $-II$: Angle bisectors of two intersecting lines are always perpendicular to each other.
- ABoth the Statements are true and Statement $-II$ is the correct explanation of the Statement $-I$.
- BBoth the Statements are true but Statement $-II$ is not the correct explanation of the Statement $-I$.
- CStatement $-I$ is true and Statement $-II$ is false.
- DStatement $-I$ is false and Statement $-II$ is true.
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Similar Questions
The equation of bisectors of the angles between the lines $|x| = |y|$ are
Medium
View SolutionLines $L_1: y-x=0$ and $L_2: 2x+y=0$ intersect the line $L_3: y+2=0$ at $P$ and $Q$,respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersects $L_3$ at $R$.
$STATEMENT-1$ : The ratio $PR:RQ$ equals $2\sqrt{2}:\sqrt{5}$.
$STATEMENT-2$ : In any triangle,the angle bisector divides the opposite side in the ratio of the sides containing the angle.
$STATEMENT-1$ : The ratio $PR:RQ$ equals $2\sqrt{2}:\sqrt{5}$.
$STATEMENT-2$ : In any triangle,the angle bisector divides the opposite side in the ratio of the sides containing the angle.
DifficultIIT 2007
View SolutionLines $L_1: y - x = 0$ and $L_2: 2x + y = 0$ intersect the line $L_3: y + 2 = 0$ at points $P$ and $Q$ respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersects $L_3$ at $R$.
Statement-$1$: The ratio $PR:RQ$ is equal to $2\sqrt{2} : \sqrt{5}$.
Statement-$2$: In any triangle,the angle bisector divides the opposite side in the ratio of the sides containing the angle.
Statement-$1$: The ratio $PR:RQ$ is equal to $2\sqrt{2} : \sqrt{5}$.
Statement-$2$: In any triangle,the angle bisector divides the opposite side in the ratio of the sides containing the angle.
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View SolutionGiven vertices $A(1, 1)$,$B(4, -2)$,and $C(5, 5)$ of a triangle,find the equation of the line perpendicular to the internal angle bisector of $\angle A$ and passing through vertex $C$.
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View SolutionThe equations of the angle bisectors between the $x$-axis and $y$-axis are:
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