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Question Number 217686 by mnjuly1970 last updated on 18/Mar/25

Commented by mnjuly1970 last updated on 18/Mar/25

$w h y B C = C F ? ⇑⇑⇑$ $a n d f i n d t h e v a l u e o f^{″} x^{″} .$
Commented by mr W last updated on 18/Mar/25

$y o u m e a n t B C = B F ?$
Commented by mnjuly1970 last updated on 18/Mar/25

$y e s y e s s i r . m y m i s t a k e . . \underset{―}{\underset{⏟}{⋚}}$
	Answered by mr W last updated on 19/Mar/25

	Commented by mr W last updated on 19/Mar/25

	$i n Δ A D E :$ $45 ° + β + α = 90 °$ $\Rightarrow β + α = 45 °$ $i n Δ C B F :$ $α + β = 45 ° \Rightarrow B C = B F = 3$ $C A = \sqrt{5^{2} + 3^{2}} = \sqrt{34}$ $s a y R = r a d i u s o f q u a r t e r c i r c l e$ $\frac{E D}{D C + C A} = \frac{C B}{B A}$ $\frac{R}{R + \sqrt{34}} = \frac{3}{5}$ $\Rightarrow R = \frac{3 \sqrt{34}}{2}$ $\frac{A E}{E D} = \frac{C A}{C B}$ $\frac{x + 3 + 5}{\frac{3 \sqrt{34}}{2}} = \frac{\sqrt{34}}{3}$ $\Rightarrow x = 9 ✓$
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