Solution: area of triangle ABC = ½ * base * height
= ½ * AB * CD
= ½ (c * p) …… (1)
Also the area of triangle ABC can also be equal to,
= ½ * base * height
= ½ * BC * AC
= ½ (a * b) …… (2)
From eq(1) and (2), we get
½ cp = ½ ab
= p = ab/c
= 1/p = c/ab
Squaring both sides, we get
\[\frac{1}{p^2}=\frac{c^2}{a^2b^2}=\frac{b^2+a^2}{a^2b^2}\]
\[\frac{1}{p^2}=\frac{b^2}{a^2b^2}=\frac{a^2}{a^2b^2}\]
\[\frac{1}{p^2}=\frac{1}{a^2}=\frac{1}{b^2}\]