F.5 maths circle

2014-10-19 9:40 am

1a. Fig.1 shows the cross-section of a tunnel. The cross-section is constructed by a circle with the lower segment removed. The width of the lane AB is 12m. The
height of the tunnel is 13m. Find the radius of the circle.
Picture of fig.1: http://postimg.org/image/6ptkoo0wv/

b. Fig.2 shows the cross-section of another tunnel. The cross-section is
constructed by a circle with the upper and lower segments removed. The widths of the ceiling PQ and the lane RS are8m and 12m respectively. The height of the
tunnel is 10m. Find the radius of the circle. (Assume that PQ and RS are parallel to each other.)
Picture of fig.2: http://postimg.org/image/7zb1c9szx/

I don't have any ideas for the questions. Please help!

回答 (1)

知足常樂

2014-10-19 9:57 am

✔ 最佳答案

圖片參考：https://s.yimg.com/rk/HA00430218/o/74052610.png

(a)
Read Fig. I.

6² + (13 - r)² = r²

36 + 169 - 26r + r² = r²

26r = 205

r = 205/26

(b)
Read Fig. II.

√(r² - 4²) + √(r² - 6²) = 10

√(r² - 16) = 10 - √(r² - 36)

r² - 16 = 100 - 20√(r² - 36) + r² - 36

-16 = 100 - 20√(r² - 36) - 36

20√(r² - 36) = 100 - 36 + 16

20√(r² - 36) = 80

√(r² - 36) = 4

r² - 36 = 16

r² = 52

r = 2√13 or -2√13 (rejected)

2014-10-19 10:43:47 補充：
Q
Why are they perpendicular?

A
"line from centre perpendicular chord bisects chord"

2014-10-19 10:44:34 補充：
Sorry, 應該係:
"line joining centre to midpoint of chord perpendicular to chord"
才對

2014-10-19 16:59:29 補充：
邏輯倒轉了。

我是先定義 mid-point M
那麼 AM = 6 (m)
然後因為 line joining centre to midpoint of chord perpendicular to chord
所以得知 AM ⊥ OM

👍 0 👎 0