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Question Number 199672 by Mingma last updated on 07/Nov/23

	Answered by mr W last updated on 07/Nov/23

	Commented by mr W last updated on 07/Nov/23

	${(a + 4)}^{2} + {(a + 8)}^{2} = {(2 a + 4)}^{2}$ $a^{2} - 4 a - 32 = 0$ $(a + 4) (a - 8) = 0$ $\Rightarrow a = 8$ $a r e a A B C = \frac{(8 + 4) (8 + 8)}{2} = 96$
	Commented by necx122 last updated on 07/Nov/23
	Mr. w, please, I'll love to know how (a+4) came about, sir
	Commented by cortano12 last updated on 07/Nov/23

	${\underset{―}{\underset{⏟}{}}}^{}$
	Commented by mr W last updated on 07/Nov/23

	$t o n e c x 122 s i r :$ $S a y O = c e n t e r o f c i r c l e$ $C F = E O = 4$ $C E = F O = 4$ $O F = 4 = C F$ $∠ O B F = x = ∠ F A C$ $\Rightarrow Δ A C F \equiv Δ B F O$ $\Rightarrow B F = A C = a + 4$ $s i m i l a r l y$ $B P = A C = a + 4$
	Commented by necx122 last updated on 07/Nov/23
	Oh that's true. They are similar triangles. Thank you sir. It's clear now.
	Commented by Mingma last updated on 07/Nov/23
	Nice solution, sir!
	Commented by mr W last updated on 07/Nov/23

	$t h e y a r e n o t o n l y s i m i l a r, b u t a l s o$ $c o n g r u e n t!$
	Commented by necx122 last updated on 07/Nov/23
	Yes, that's true. Thank you.
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