Question

泰泰

點、直線與圓的關係
有兩小題，求解🙇‍♀️

晶2. 如圖,圓 的半徑為5,圓內坊簡形
45C2,已知AB5 的長比 CD 的長多2,
但 4 的弦心四 嘿比 想的陛C蘆人
闊4.,雪:                          (新和名校)
(0太與 戰的長 (5
(2) 梯形 48CP 的面積   號 全)

解歡

Answer 1

Ny-Ålesund

(僅供參考)

AB = CD + 2
OE = OF - 1
令 CD = x、OF = y，則 AB = (x+2)、OE = (y-1)

[(x+2)/2]^2 + (y-1)^2 = 25
(x^2 + 4x + 4)/4 + (y^2 - 2y + 1) = 25
x^2 + 4x + 4 + 4y^2 - 8y + 4 = 100
x^2 + 4y^2 + 4x - 8y = 92 ...(1)

(x/2)^2 + y^2 = 25
(x^2)/4 + y^2 = 25
x^2 + 4y^2 = 100 ...(2)

(1) - (2)
4x - 8y = -8
x - 2y = -2 ...(3)
兩邊平方
x^2 - 4xy + 4y^2 = 4 把(2)代入
100 - 4xy = 4
4xy = 96, xy = 24 ...(4)

(3)=> x = 2y - 2 代入(4)
y(2y - 2) = 24
2y^2 - 2y - 24 = 0
y^2 - y - 12 = 0
(y - 4)(y + 3) = 0
y = 4 or -3(不合) => x = 6

=> AB = 8、CD = 6、OE = 3、OF = 4

泰泰

辛苦了!謝謝