AP EAMCET · Maths · Straight Lines
The lines \(L_1: y-x=0\) and \(L_2: 2 x+y=0\) intersect the line \(L_3: y+2=0\) at \(P\) and \(Q\) respectively. The bisector of the acute angle between \(\mathrm{L}_1\) and \(\mathrm{L}_2\) intersects \(\mathrm{L}_3\) at \(\mathrm{R}\).
Statement 1: PR : RQ \(=2 \sqrt{2}: \sqrt{5}\)
Statement 2: In any triangle, the bisector of an angle divides the triangle into two similar triangles.
- A Statement-1 is true, Statement-2 is false
- B Statement-1 is false, Statement- 2 is true
- C Statement-1 and Statement-2 are both true
- D Statement-1 and Statement- 2 are both false
Answer & Solution
Correct Answer
(A) Statement-1 is true, Statement-2 is false
Step-by-step Solution
Detailed explanation
Given: \(\mathrm{L}_1: y-x=0\) \(\begin{aligned} & \mathrm{L}_2: 2 x+y=0 \\ & \mathrm{~L}_3=y+2=0\end{aligned}\) Solving \(\mathrm{L}_1\) and \(\mathrm{L}_3\), we get \(x=-2, y=-2 \Rightarrow p(x, y)=(-2,-2)\) Solving \(\mathrm{L}_2: 2 x+y=0 \& \mathrm{~L}_3: y+2=0\), we get…
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