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AP EAMCET · Maths · Properties of Triangles

If \(\alpha, \beta, \gamma\) are the lengths of the tangents from the vertices of a triangle to its incircle. Then

  1. A \(\alpha+\beta+\gamma=\frac{1}{r^2}(\alpha \beta \gamma)\)
  2. B \(\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}=r(\alpha \beta \gamma)\)
  3. C \(\alpha+\beta+\gamma=\frac{1}{r}(\alpha \beta \gamma)\)
  4. D \(\alpha^2+\beta^2+\gamma^2=\frac{2}{r}(\alpha \beta \gamma)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\alpha+\beta+\gamma=\frac{1}{r^2}(\alpha \beta \gamma)\)

Step-by-step Solution

Detailed explanation

It is given that \(\alpha, \beta, \gamma\) are the length of tangents from the vertices of a triangle to its incircle. Semi-perimeter of \(\triangle A B C\),…