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TS EAMCET · Maths · Properties of Triangles

If \(A B C\) is an isosceles triangle with base \(B C\), then \(r r_1=\)

  1. A \(R^2 \cos ^2 A\)
  2. B \(\frac{a^2}{2}\)
  3. C \(\frac{r}{R}\)
  4. D \(R^2 \sin ^2 A\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(R^2 \sin ^2 A\)

Step-by-step Solution

Detailed explanation

\(r=\frac{\Delta}{s}, r_1=\frac{\Delta}{s-a}\) \(\begin{aligned} & r r_1=\frac{\Delta^2}{s(s-a)} \\ & =\frac{s(s-a)(s-b)(s-c)}{s(s-a)}\end{aligned}\) \(=(s-b)(s-c)=(s-b)^2 \quad(\because {~b}={c})\) \(=\frac{(2 s-2 b)^2}{4}\)…