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ABC is a right traingle, right angled at C. if P is the length of perpendicular from C to AB and AB=c, BC=a and CA=b, then prove that (i) pc=ab (ii) `1/(p^(2)) = 1/(a^(2))+1/b^(2)`

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To solve the problem, we will prove two statements regarding triangle ABC, which is a right triangle with the right angle at C. We will denote the lengths as follows: AB = c, BC = a, and CA = b. The length of the perpendicular from C to AB is denoted as P. ### Step-by-Step Solution: **(i) Prove that \( p \cdot c = a \cdot b \)** 1. **Calculate the Area of Triangle ABC:** The area of triangle ABC can be calculated using the base and height. Here, we can take AB as the base and the height from C to AB (which is P). ...
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