AP EAMCET · Maths · Straight Lines
If \(\triangle \mathrm{ABC}\) is a right angled isosceles triangle and \(\angle \mathrm{C}=90^{\circ}\), then \(\mathrm{r}: \mathrm{r}_3=\)
- A \(\sqrt{2}+1: \sqrt{2}-1\)
- B \(\sqrt{2}-1: \sqrt{2}+1\)
- C \(\sqrt{2}: 1\)
- D \(1: \sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{2}-1: \sqrt{2}+1\)
Step-by-step Solution
Detailed explanation
\(\because A B C\) is isosceles triangle. \(\therefore A C=B C\) and \(\angle C=90^{\circ}\) Let \(A C=B C \Rightarrow a=b\) In \(\triangle A B C\), \(\begin{aligned} & c^2=a^2+b^2=a^2+a^2=2 a^2 \\ & \Rightarrow \quad c=a \sqrt{2} \end{aligned}\) Now,…
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