TS EAMCET · Maths · Properties of Triangles
Let \(\mathrm{p}_1, \mathrm{p}_2, \mathrm{p}_3\) be the altitudes of a triangle ABC drawn through the vertices \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) respectively. If \(r_1=4, r_2=6, r_3=12\) are the ex-radii of triangle ABC then \(\frac{1}{\mathrm{p}_1^2}+\frac{1}{\mathrm{p}_2^2}+\frac{1}{\mathrm{p}_3^2}=\)
- A \(\frac{25}{72}\)
- B \(\frac{25}{144}\)
- C \(\frac{25}{288}\)
- D \(\frac{25}{216}\)
Answer & Solution
Correct Answer
(C) \(\frac{25}{288}\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{r} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}\) \(\frac{1}{r} = \frac{1}{4} + \frac{1}{6} + \frac{1}{12} = \frac{3+2+1}{12} = \frac{6}{12} = \frac{1}{2}\) \(\frac{1}{r^2} = \left(\frac{1}{2}\right)^2 = \frac{1}{4}\)…
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