AP EAMCET · Maths · Properties of Triangles
In \(\triangle \mathrm{ABC}\), if \(\angle \mathrm{A}=90^{\circ}\), then \(\left(\mathrm{r}_2-\mathrm{r}_1\right)\left(\mathrm{r}_3-\mathrm{r}_1\right)=\)
- A \(\mathrm{r}_2 \mathrm{r}_3\)
- B \(2 r_2 r_3\)
- C \(4 r_2 r_3\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(2 r_2 r_3\)
Step-by-step Solution
Detailed explanation
In \(\triangle \mathrm{ABC} \angle \mathrm{A}=90^{\circ}\) \(\begin{aligned} & \Rightarrow b^2+c^2=a^2 \\ & \Rightarrow \frac{1}{2}(b+c-a)^2=(b-a)(c-a) \\ & \Rightarrow(b-a)(c-a)=2(s-a)^2 \\ & \Rightarrow \frac{(b-a)(c-a)}{(s-a)^2}=2 \end{aligned}\)…
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