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108會考數學試題_24


<單選題>圖(十七)圓上\(A\)、\(B\)、\(C\)、\(D\)四點,Image$ \widehat{AD}=180^\circ$,\(\widehat{AB}=\widehat{BD}\)、\(\widehat{BC}=\widehat{CD}\),\(P\)在\(\widehat{AB}\)、\(Q\)在\(\widehat{BD}\),\(\angle APQ=130^\circ\),下列敘述何者正確?
(A)\(Q\)點在\(\widehat{BC}\)上,且\(\widehat{BQ}\gt\widehat{QC}\)
(B)\(Q\)點在\(\widehat{BC}\)上,且\(\widehat{BQ}\lt\widehat{QC}\)
(C)\(Q\)點在\(\widehat{CD}\)上,且\(\widehat{CQ}\gt\widehat{QD}\)
(D)\(Q\)點在\(\widehat{CD}\)上,且\(\widehat{CQ}\lt\widehat{QD}\)

答案

B


計算弧長得\(\widehat{BQ}=10^\circ\)、\(\widehat{QC}=35^\circ\),故\(Q\)在\(\widehat{BC}\)上且\(\widehat{BQ}<\widehat{QC}\)。


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