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AP EAMCET · Maths · Properties of Triangles

If \(P_1, P_2\) and \(P_3\) are the lengths of the altitudes drawn from the vertices \(A, B\) and \(C\) of \(\triangle A B C\) respectively, then \(\frac{\cos A}{P_1}+\frac{\cos B}{P_2}+\frac{\cos C}{P_3}=\)

  1. A \(\frac{1}{\mathrm{R}}\)
  2. B \(\mathrm{R}\)
  3. C \(\frac{\Delta}{\mathrm{R}}\)
  4. D \(\frac{r}{R}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{\mathrm{R}}\)

Step-by-step Solution

Detailed explanation

We know that: \[ P_1=\frac{2 \Delta}{a}, P_2=\frac{2 \Delta}{b}, P_3=\frac{2 \Delta}{c} \] Now, \(\frac{\cos A}{P_1}+\frac{\cos B}{P_2}+\frac{\cos C}{P_3}\)…