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Question Number 23262 by ajfour last updated on 28/Oct/17

Commented by ajfour last updated on 28/Oct/17

$\frac{C N}{A C} = \frac{x}{x + y}; \frac{A N}{A C} = \frac{y}{x + y}$ $\frac{M B}{A B} = \frac{y}{x + y}; \frac{A M}{A B} = \frac{x}{x + y} .$ $b a s e d o n s i m i l a r i t y o f t r i a n g l e s .$ $△ C N P \sim △ C A B$ $\Rightarrow \frac{C N}{A C} = \frac{N P (= A M)}{A B} = \frac{C P}{B C}$ $I f A B = a a n d A C = b, t h e n$ $\Rightarrow \frac{C N}{b} = \frac{A M}{a} = \frac{x}{x + y}$ $\Rightarrow C N = (\frac{x}{x + y}) b; A M = (\frac{x}{x + y}) a$ $A N = A C - C N = b - \frac{b x}{x + y} = (\frac{y}{x + y}) b$ $M B = A B - A M = a - \frac{a x}{x + y} = (\frac{y}{x + y}) a .$
Commented by ajfour last updated on 28/Oct/17

$E x p l a n a t i o n t o a q u e r y r e l a t e d t o$ $Q . 23251$
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