Question

∆ABC is right angled at C , if P is the length of the perpendicular from C to AB and a,b,c are the length of the sides opposite amgle A , angle B and angle c respectively then prove that 1/p^2=1/a^2+1/b^2​

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Answer 1

Step-by-step explanation:

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Answer 2

To prove : $\frac{1}{p^2}= \frac{1}{a^2}+\frac{1}{b^2}$

Explanation:

here ,

area of the triangle ABC  

$\frac{1}{2}\times BC \times AC \\\\ \frac{1}{2}\times a \times b \\\\\frac{ab}{2} \\\\area = \frac{1}{2} \times CD\times AB \\\\\frac{1}{2} \timesp \times c = \frac{pc}{2}\\\\ab = pc \\\\c = \frac{ab}{p}\\\\AB = \frac{ab}{p}$

thus , in triangle ABC using Pythagoras theorem

$AB^2= AC^2 + BC ^2 \\\\(\frac{ab}{p})^2= b^2+a^2\\\\\frac{1}{p^2}= \frac{b^2 +a^2}{a^2+b^2}\\\\\frac{1}{p^2}= \frac{1}{a^2}+\frac{1}{b^2}$

hence proved

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