S A B C = p ( p − a ) ( p − b ) ( p − c ) S_{ABC}=\sqrt{\smash[b]{p(p-a)(p-b)(p-c)}} S A BC = p ( p − a ) ( p − b ) ( p − c )
p = a + b + c 2 p={a+b+c \over 2} p = 2 a + b + c
A B = a = 50 , B C = b = 63 , A C = c = 42 AB=a=50, BC=b=63, AC=c=42 A B = a = 50 , BC = b = 63 , A C = c = 42
p = 50 + 63 + 42 2 = 155 2 = 77.5 p={50+63+42 \over 2}={155 \over 2}=77.5 p = 2 50 + 63 + 42 = 2 155 = 77.5
S A B C = 77.5 ∗ ( 77.5 − 50 ) ∗ ( 77.5 − 63 ) ∗ ( 77.5 − 42 ) S_{ABC}=\sqrt{\smash[b]{77.5 \ast (77.5-50) \ast (77.5-63) \ast (77.5-42)}} S A BC = 77.5 ∗ ( 77.5 − 50 ) ∗ ( 77.5 − 63 ) ∗ ( 77.5 − 42 )
S A B C = 1.25 ∗ 702119 S_{ABC}=1.25 \ast \sqrt{702119} S A BC = 1.25 ∗ 702119
S A B C = S A B O + S O B C = R ∗ A B 2 + R ∗ B C 2 S_{ABC}=S_{ABO}+S_{OBC}={R \ast AB \over 2}+{R \ast BC \over 2} S A BC = S A BO + S OBC = 2 R ∗ A B + 2 R ∗ BC
S A B C = 50 ∗ R 2 + 63 ∗ R 2 = 113 ∗ R 2 S_{ABC}={50 \ast R \over 2}+{63 \ast R \over 2}={113 \ast R \over 2} S A BC = 2 50 ∗ R + 2 63 ∗ R = 2 113 ∗ R
113 ∗ R 2 = 1.25 ∗ 702119 {113 \ast R \over 2}=1.25 \ast \sqrt{702119} 2 113 ∗ R = 1.25 ∗ 702119
R = 10 ∗ 702119 452 ≈ 18.5 R={10 \ast \sqrt{702119} \over 452} \approx 18.5 R = 452 10 ∗ 702119 ≈ 18.5
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