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Question Number 193037 by DAVONG last updated on 02/Jun/23

	Answered by Subhi last updated on 02/Jun/23

	${D C}^{2} = D B . A D$ $20^{2} = D B . (9 + D B)$ ${D B}^{2} + 9 D B - 400 = 0$ $D B = 16$ $\frac{16}{s i n (D C B)} = \frac{20}{s i n (D B C)} (s i n l a w)$ $\frac{s i n (D C B)}{s i n (D B C)} = \frac{16}{20} = \frac{4}{5}$ $D \hat{C B} = B \hat{A C} (T h e s a m e a r c)$ $s i n (D \hat{C B}) = s i n (B \hat{A C})$ $180 - D \hat{B C} = A \hat{B C}$ $s i n (180 - D \hat{B C}) = s i n (D \hat{B C}) = s i n (A \hat{B C})$ $\frac{s i n (D C B)}{s i n (D B C)} = \frac{s i n (B A C)}{s i n (A B C)} = \frac{4}{5}$ $\frac{B C}{s i n (B A C)} = \frac{A C}{s i n (A B C)}$ $\frac{B C}{A C} = \frac{s i n (B A C)}{s i n (A B C)} = \frac{4}{5}$
	Commented by York12 last updated on 03/Jun/23

	$s i r w h e r e a r e y o u f r o m$
	Commented by Subhi last updated on 03/Jun/23

	$E g y p t, s i r$
	Answered by HeferH last updated on 02/Jun/23

	$s a y : B C = a, A C = b, B D = x$ $20^{2} = x (9 + x)$ $x^{2} + 25 x - 16 x - 400 = 0$ $(x - 16) (x + 25) = 0$ $x = 16$ $\frac{a}{b} = \frac{20}{9 + x} = \frac{20}{25} = \frac{4}{5}$
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