配套习题- 判定切线的解题策略 -【青果学院】

挑战习题

1/5单选题

难度：

1.有下列结论：（1）平分弦的直径垂直于弦；（2）圆周角的度数等于圆心角的一半；（3）等弧所对的圆周角相等；（4）经过三点一定可以作一个圆；（5）三角形的外心到三边的距离相等；（6）垂直于半径的直线是圆的切线. 其中正确的个数为（）

A	1个
B	2个
C	3个
D	4个

提示1：: IOagueaNruWeguW+hOWumueQhuWSjOWchuWRqOinkuWumueQhuaOqOaWre+8mw==

提示2：: IOagueaNruWIh+e6v+eahOWIpOWumuWumueQhu+8mw==

提示3：: IOagueaNruehruWumuWchueahOadoeS7tg==

正确答案：QQ==

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2/5单选题

难度：

已知：如图，AB是⊙O的直径，点P在BA的延长线上，弦CD交AB于E，连接OD、PC、BC，∠AOD=2∠ABC，∠P=∠D，过E作弦GF⊥BC交圆与G、F两点，连接CF、BG. 则下列结论：
①CD⊥AB；②PC是⊙O的切线；③OD∥GF；④弦CF的弦心距等于BG. 则其中正确的是（）

A	①②④
B	③④
C	①②③
D	①②③④

提示1：: PHA+6L+e5o6lQkTjgIFPQ+OAgUFH77yM6L+HT+S9nE9R4oqlQ0bkuo5R77yMT1riiqVCR+S6jlrvvIzmoLnmja7lnoLlvoTlrprnkIbmsYLlh7riiKBBQkM94oigQUJE77yM5rGC5Ye6PGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzAwLzRGL3JCQUNGRk1NVDN1aWRPVGxBQUFCTWpjSjdHNDUwMi5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvMDAvNEYvckJBQ0ZGTU1UM3VpZE9UbEFBQUJNamNKN0c0NTAyLnBuZyIgaGVpZ2h0PSIyNSIgd2lkdGg9IjI0Ij49PGltZyBzcmM9Imh0dHBzOi8vcDEucWluZ2d1by5jb20vRzEvTTAwLzIzLzNEL3JCQUNFMU1NVDN2eTNHbmtBQUFCSEJyVWdQbzAxNy5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMS5xaW5nZ3VvLmNvbS9HMS9NMDAvMjMvM0QvckJBQ0UxTU1UM3Z5M0dua0FBQUJIQnJVZ1BvMDE3LnBuZyIgaGVpZ2h0PSIyNSIgd2lkdGg9IjI0Ij7vvJs8L3A+

提示2：: PHA+5rGC5Ye64oigUCviiKBQQ0Q9OTDCsOWSjOKIoFA94oigRENP5Y2z5Y+v5rGC5Ye6UEPmmK/lnIbnmoTliIfnur/vvJs8L3A+

提示3：: PHA+6YeH55So5Y+N6K+B5rOV5rGC5Ye64oigQj0zMMKw77yM5L2G5bey55+l5rKh5pyJ57uZ5Ye65q2k5p2h5Lu277yM5Y2z5Y+v5Yik5pat4pGi77ybPC9wPg==

提示4：: PHA+5rGC5Ye6Q0Y9QUfvvIzmjqjlh7pDUT1PWu+8jOivgeKWs09DUeKJjOKWs0JPWu+8jOaOqOWHuk9RPUJa77yM5Y2z5Y+v5Yik5pat4pGjLjwvcD4=

正确答案：QQ==

PHA+PGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwL0QyLzY0L3JCQUNKbFpVSFRDQnhzVWdBQUJqMVdyMEFkdzc4Ni5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvRDIvNjQvckJBQ0psWlVIVENCeHNVZ0FBQmoxV3IwQWR3Nzg2LnBuZyIgYWx0PSIiIHN0eWxlPSJ3aWR0aDogNDAycHg7IGhlaWdodDogNjQ3cHg7Ij48YnI+PC9wPg==

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3/5单选题

难度：

如图，在⊙O中，E是半径OA上一点，射线EF⊥OA，交圆于B，P为EB上任一点，射线AP交圆于C，D为射线BF上一点，且DC=DP，下列结论：①CD为⊙O的切线；②PA＞PC；③∠CDP=2∠A，其中正确的结论有（）

A	3个
B	2个
C	1个
D	0个

提示1：: PHA+5qC55o2u6KeS5bqm5LmL6Ze055qE6L2s5o2i5rGC4oigT0NBK+KIoERDUD05MMKw6K+B5YiH57q/77ybPC9wPg==

提示2：: PHA+5qC55o2u5LiJ6KeS5b2i55qE5YaF6KeS5ZKM5rGC6KeS5bqm5LmL6Ze055qE5YWz57O744CCPC9wPg==

正确答案：Qg==

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4/5单选题

难度：

如图，圆内接△ABC的外角∠ACH的平分线与圆交于D点，DP⊥AC，垂足是P，DH⊥BH，垂足是H，下列结论：①CH=CP；②AD=DB；③AP=BH；④DH为圆的切线. 其中一定成立的是（）

A	①②④
B	①③④
C	②③④
D	①②③

提示1：: PHA+6L+e5o6lQkQuIOivgeKWs1BDROKJjOKWs0hDRO+8iEhM77yJ5b6XQ0g9Q1DvvJs8L3A+

提示2：: PHA+6K+B5piO4pazQURQ4omM4pazQkRI77yIQUFT77yJ5b6XQUQ9RELvvJs8L3A+

提示3：: PHA+QVA9QkjvvIzml6Dms5Xor4HmmI5ESOS4uuWchueahOWIh+e6vzwvcD4=

正确答案：RA==

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5/5单选题

难度：

如图，△ABC中，AB=AC，以AB为直径的⊙O交AC于E，交BC于D，DF⊥AC于F. 给出以下五个结论：①BD=DC；②CF=EF；③=；④∠A=2∠FDC；⑤DF是⊙O的切线. 其中正确的有（）

A	5个
B	4个
C	3个
D	2个

提示1：: PHA+6aaW5YWI55SxQULmmK/iiplP55qE55u05b6E77yM5b6X5Ye6QUTiiqVCQ++8jOaOqOWHukJEPURD77ybPC9wPg==

提示2：: PHA+55SxT0E9T0LvvIzmjqjlh7pPROaYr+KWs0FCQ+eahOS4reS9jee6v++8jOW+l0RG4oqlT0TvvIzljbNERuaYr+KKmU/nmoTliIfnur/vvJs8L3A+

提示3：: PHA+55SxREbiiqVBQ++8jEFE4oqlQkPvvIzmjqjlh7rilrNDREXkuLrnrYnohbDkuInop5LlvaLvvIzku47ogIzmjqjlh7riiKBBPTLiiKBGREPvvIxDRj1FRi48L3A+

正确答案：Qg==

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