Question-213550

Question Number 213550 by mr W last updated on 08/Nov/24

Commented by mr W last updated on 08/Nov/24

s e m i c i r c l e

Answered by A5T last updated on 08/Nov/24

Commented by A5T last updated on 08/Nov/24

\frac{s - 3}{2} = r - 3 \Rightarrow s = 2 r - 3

\frac{t - 6}{2} = r - 6 \Rightarrow t = 2 r - 6

{(t - 6)}^{2} + {(s - 3)}^{2} = {(2 r)}^{2} = 4 r^{2}

\Rightarrow {(2 r - 12)}^{2} + {(2 r - 6)}^{2} = 4 r^{2}

\Rightarrow r^{2} - 18 r + 45 = 0 \Rightarrow r = 3 o r 15

t - 6 > 0 \Rightarrow r = 15 \Rightarrow 2 r = 30

Commented by mr W last updated on 08/Nov/24

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Answered by Spillover last updated on 09/Nov/24

R²=[R -6]²+ [R -3]²
R² -12R +36 + R² -6R +9
R²=2R² -18R +45 R² -18R +45=0
R=[18+[324 – 180]½]/2

R=[18+12]/2=15
EF=[15+15]=30