TS EAMCET · Maths · Properties of Triangles
Assertion (A): In \(\triangle A B C\), if \(r=6, r_2=36, R=15\) then \(c^2+a^2=b^2\) Reason (R): In \(\triangle A B C\), if \(r: R: r_2=1: 2.5: 6\) then \(\mathrm{B}=90^{\circ}\) The correct option among the following is
- A Both (A) and (R) are true. (R) is a correct explanation of (A)
- B Both (A) and (R) are true, but (R) is not a correct explanation of (A)
- C (A) is true and (R) is false
- D (A) is false and (R) is true
Answer & Solution
Correct Answer
(A) Both (A) and (R) are true. (R) is a correct explanation of (A)
Step-by-step Solution
Detailed explanation
(R) Given that \(\mathrm{r}: \mathrm{R}: \mathrm{r}_2=1: 2.5: 6=2: 5: 12\) \(\Rightarrow \mathrm{r}=2 \mathrm{k}, \mathrm{R}=5 \mathrm{k}\) and \(\mathrm{r}_2=12 \mathrm{k}\) we have \(r_2-r=4 R \sin ^2 \frac{B}{2}\)…
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