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Question Number 204890 by mr W last updated on 29/Feb/24

Commented by mr W last updated on 29/Feb/24

$A B C D i s a s q u a r e w i t h s i d e l e n g t h 2 .$ $E i s m i d p o i n t o f C D, F i s m i d p o i n t$ $o f A D . f i n d A P .$
	Answered by Frix last updated on 01/Mar/24

	$A = (- 1 ∣ - 1), B = (1 ∣ - 1), C = (1 ∣ 1), D = (- 1 ∣ 1)$ $E = (0 ∣ 1); F = (- 1 ∣ 0)$ $B E : y = - 2 x + 1; C F : y = \frac{x}{2} + \frac{1}{2} \Rightarrow P = (\frac{1}{5} ∣ \frac{3}{5})$ $\Rightarrow ∣ A P ∣=∣ (\frac{6}{5} ∣ \frac{8}{5}) ∣= 2$
	Commented by mr W last updated on 01/Mar/24
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	Answered by mr W last updated on 01/Mar/24

	Commented by mr W last updated on 01/Mar/24

	$w e c a n e a s i l y p r o v e t h a t B E ⊥ C F .$ $\Rightarrow A B P F i s c y c l i c .$ $∠ A P B = ∠ A F B = ∠ B E C = ∠ A B P$ $\Rightarrow Δ A B P i s i s o s c e l e s .$ $\Rightarrow A P = A B = 2 ✓$
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