F4 Properties of Circle

[匿名]

2011-03-13 6:45 am

Properties of circles1. The figure shows a broken circular compact disc. Given that AB=9cm and CD=2cm.

-> Find the diameter of the compact disc. (with proof/reference)

2. In the figure, PQ and RS are two parallel chords. Given that PQ=12cm, RS = 5cm and the distance from O to the chord PQ is 2.5 cm, find, with proof

a. the radius of circle
b. the distance between PQ and RS

http://upload.lsforum.net/users/public/n51242online_imagez93.jpg

圖片參考：http://upload.lsforum.net/users/public/n51242online_imagez93.jpg

回答 (1)

用戶2053

2011-03-13 9:10 pm

✔ 最佳答案

1)Let r be the radius ,
OD ⊥ AB (line joining centre to mid-pt. of chord⊥chord)
AD = AB/2 (line from centre⊥chord bisects chord)So △OAD is a Right-angled triangle.OA² = OD² + AD²
r² = (OC - CD)² + (9/2)²
r² = (r - 2)² + (9/2)²
r² = r² - 4r + 4 + (9/2)²
4r = 4 + 81/4
r = 97/16The diameter of the compact disc
= 2r
= 2 * 97/16
= 97/8 cm 2a)Let r be the radius ,
m be the mid point of RS ,
M be the mid point of PQ .OM ⊥ PQ (line joining centre to mid-pt. of chord⊥chord)
PM = QM (line from centre⊥chord bisects chord)So △OPM is a Right-angled triangleOP² = OM² + PM²
r² = 2.5² + (12/2)²
r = 6.5 cmb)Om ⊥ RS (line joining centre to mid-pt. of chord⊥chord)
Rm = Sm (line from centre⊥chord bisects chord)So △ORm is a Right-angled triangleOR² = Om² + Rm²
r² = Om² + (5/2)²
6.5² = Om² + (5/2)²
Om = 6 cmThe distance between PQ and RS
= Om - OM
= 6 - 2.5
= 3.5 cm

👍 0 👎 0