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円と円の外接線の求め方
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Sho Iizuka
June 14, 2014
Programming
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70
円と円の外接線の求め方
https://www.slideshare.net/kujira16/ss-35861169
Sho Iizuka
June 14, 2014
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Transcript
ԁͱԁͷ֎ઢ !TIPSB@LVKJSB
w *$1$ͷزԿϥΠϒϥϦղઆγϦʔζͦͷͰ͢ w ԁͱԁͷަʹҾ͖ଓ͖ɺԁͱԁͷ֎ઢͷٻΊํ Α͔͘Βͳ͔ͬͨͷͰɺࣗͷཧղͷͨΊʹ·ͱΊ ͓͖ͯ·͢ w ࢀߟʹͨ͠ϥΠϒϥϦ w L@PQFSBGBO͞Μ
ʢݱࡏͲ͜ͰμϯϩʔυͰ͖Δͷ͔ෆ໌ʣ w X ͞Μ
֎ઢ
ઢ
ଋࣄ Q Q S S $ $
֎ઢͷٻΊํ w SSͷ߹ͷํ w $ͷͱ$ͷΛ݁Ϳઢʢʹઢʣ͕ ઢQQͱฏߦʹͳΔͷͰɺSPUͳͲΛͬͯ ͕ΜΔʢ؆୯ͳͷͰৄ͍͠ղઆলུʣ w S㱠Sͷ߹ͷํ w
ຊͷ֎ઢͷަRΛٻΊ͔ͯΒUBOHFOU$1Ͱ $͓Αͼ$ͱͷΛٻΊΔ
S㱠Sͷ߹ R
S㱠Sͷ߹ R S S U E θ
ઢ U S ͔ΒͳΔ֯ࡾ֯ܗͱ ઢ U E S ͔ΒͳΔ֯ࡾ֯ܗʹ͓͍ͯ ֯ВΛڞ༗͍ͯ͠ΔͷͰTJOВ͕͘͠ͳΔ
r1 t = r2 t + d t = r1d r2 r1
RͷҐஔΛಘΔʹ QΛ࢝ͱͯ͠ɺQˠQͷ୯ҐϕΫτϧΛ ͞U͚ͩ৳ͤྑ͍ q = p1 + t · p1
p2 d = p1 + r1d r2 r1 · p1 p2 d = p1 (r2 r1 ) r2 r1 + r1 (p1 p2 ) r2 r1 = p1 r2 p2 r1 r2 r1
2R͕$ଆͰͳ͘$ଆʹ͋Δ߹ʁ "͏·͍͔͘ͳ͍Α͏ͳؾ͕͢Δ͕ɺ ಋग़ͯ͠ΈΔͱಉࣜ͡ͰQͷҐஔΛද͢͜ͱ͕Ͱ͖ Δ͜ͱ͕͔Δ
ઢͷٻΊํ w ർΕ͖ͯͨͷͰলུ͢Δ͕ɺ֓ཁҎԼͷͱ͓Γ w ઢͱઢQQͷަΛRͱ͠ɺQͱRͷڑΛUͱ͢Δ w ઢͱઢQQ͕ަΘ͍ͬͯΔ෦ʹ͓͍ͯɺର֯В ͕͍͠ʹTJOВ͕͍͜͠ͱ͔ΒSUS EU
w UΛܭࢉ͔ͯ͠ΒQˠQͷ୯ҐϕΫτϧΛ ͞U͚ͩ৳ͯ͠Rͷ࠲ඪΛಘΔ w Rͱ$ɺ͓ΑͼRͱ$ʹ͍ͭͯUBOHFOU$1Λܭࢉ͢Δ
ײ w ηϯλʔࢼݧྗ͕େࣄͩͱࢥ͍·ͨ͠ʢখฒײʣ w Ջ͕Ͱ͖ͨΒଓ͖Λ࡞Δ͔