F4 math problems ( Circles )

用戶3618

2007-04-12 2:18 am

In Figure, ABC and DEF are straight lines. O is the centre of the circle which passes through the points A,D,E and B. ∠AOE = 150° and ∠BEF = 78°.

(a) Find ∠EBC and ∠CFE.
(b) Show that AD // CF.

Figure http://server4.pictiger.com/img/1049858/picture-hosting/.jpg

回答 (1)

用戶236280

2007-04-12 2:36 am

✔ 最佳答案

Actually it is not too difficult ar ^_^" but the lines just make the circle a bit messy so as to confuse you

∠ADE = 1/2 ∠AOE = 75° (∠ at centre twice ∠ at circumference) <-- there is an abbreviation for circumference but i don't know how to type those symbols

∠ADE +∠ABE = 180° (opp. ∠s, cyclic quad.)
∠ABE = 105°

∠ABE + ∠EBC = 180° (adj ∠s on st. line)
∠EBC = 75° (ans)

∠EBC +∠CFE = 180° (opp. ∠s, cyclic quad.)
∠CFE = 105° (ans)

b) ∠ADE +∠CFE = 180°
therefore AD // CF (int. ∠s, supp )

done!

參考: myself + maths textbook

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