AP EAMCET · Maths · Straight Lines
If the incentre of the triangle formed by the lines \(x-2=0, x+y-1=0\), \(x-y+3=0\) is \((\alpha, \beta)\), then \(\beta=\)
- A \(2\)
- B \(\sqrt{2}+1\)
- C \(\frac{2 \sqrt{2}-1}{\sqrt{2}+1}\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
Vertices: \(A=(-1, 2), B=(2, 5), C=(2, -1)\) Side lengths: \(a = BC = \sqrt{(2-2)^2+(-1-5)^2} = 6\) \(b = AC = \sqrt{(2-(-1))^2+(-1-2)^2} = \sqrt{3^2+(-3)^2} = \sqrt{18} = 3\sqrt{2}\) \(c = AB = \sqrt{(2-(-1))^2+(5-2)^2} = \sqrt{3^2+3^2} = \sqrt{18} = 3\sqrt{2}\)…
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