Re: [問題] 數學的問題
※ 引述《ericdoctor (小黑)》之銘言:
: 請問
: 有沒有
: 給三角形三頂點座標
: 求內切圓座標的公式
: (好像不應該在國中出現這東西= =)
剛剛粗算一下好像是可以解
只是通式導出來應該就不好看了,一堆文字
因為已經給三頂點座標
取出任兩線段方程式,用內心(x,y)到三邊等距性質
可得兩條方程式,聯立解得 x & y
L:aX+bY=c , 點到線距離=(|ax+by-c|)÷(a^2+b^2)^(1/2)
...................分子=絕對值ax+by-c
(式子很醜)→ 分母=根號a平方+b平方
絕對值內的xy為要求的點座標,也是這題的圓心座標
不知道有沒有這麼複雜,有請高手幫忙來個簡單點的or速解法
不過我猜基測真的出,畫完圖應該就有解了( ̄□ ̄|||)a
: 還有
: 外切圓R公式
: R=abc/4A
: 有辦法用國中的證法證出來嗎
: 3Q~
OA=OB=OC=OD=R,OD為BC中垂線
∠BAC=1/2弧BDC=1/2∠BOC=∠BOD
BC=a
1/2BC=1/2a=OBsin∠BOD=Rsin∠BOD=Rsin∠BAC=Rsinθ
^^^^ ^^^^^^
1/2abc=bcRsinθ
1/2‧1/2abc=1/2bcRsinθ=R‧1/2‧b‧c sinθ=R‧A
R=abc/4A
圖 http://0rz.tw/bGQFw
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