Question-217686

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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