circle - Ans.fyi 參考答案

circle

2007-12-15 11:50 pm

1.In Fig. 4.76, BC is a diameter of the circle.
AP perpendicular BC, AP=6cm and AC=10cm.
a)Find the length of PC.
b)Find the radius of the circle.
http://show.simpload.com/12144763857bb6291.bmp?server=s3

2.In Fig. 4.77, AP=PB,APQ=CPQ and PRSQ is a straight line.
a)Show that AR=AS.
b)If ABC=75度 and ACP=45度,find ARS
http://show.simpload.com/1214476386af7730e.bmp?server=s3

回答 (1)

Ben Chong

2007-12-16 12:32 am

✔ 最佳答案

1(a)
10^2 - 6^2 = pc^2
pc=8

1(b)
因為bc is diameter ,所以angle CAB is 90度 (Reason 睇番書）
因triangle acp ~ triangle bca (aaa)
SO, CP/CA = CA/CB
so,bc=12.5 Radius=12.5/2 =6.25cm

2(a)
因為pb=pa
所以angle bap=angle pba (reason睇書)
所以angle ARS =apq + bap (ext.angle of triagle)
因為angle pba = angle pca (reason睇書)
所以angle ASR= angle cpq + pca (ext.angle of triangle)
因為angle ARS=ASR ,所以AR = AS (side opp.equal angle)

2(b)
apc=75度 (reason 睇書)
cpq=75/2 = 37.5度
cpq + 45 = asr (ext.angle of triangle)
asr=82.5度
因為asr=ars (proved)
所以ars=82.5度

2007-12-15 16:34:40 補充：
補充番2apca=pba

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