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            • 1. 如图所示,\(\triangle ABC\)内接于圆\(O\),\(D\)是\( \hat BAC\)的中点,\(∠BAC\)的平分线分别交\(BC\)和圆\(O\)于点\(E\),\(F\).
              \((\)Ⅰ\()\)求证:\(BF\)是\(\triangle ABE\)外接圆的切线;
              \((\)Ⅱ\()\)若\(AB=3\),\(AC=2\),求\(DB^{2}-DA^{2}\)的值.
            • 2. 如图,在\(\triangle ABC\)中,\(MN/\!/BC\),\( \dfrac {AM}{MB}= \dfrac {1}{2}\),\(MC\),\(NB\)交于点\(O\),若\(\triangle OMN\)的面积等于\(a\),得\(\triangle OBC\)的面积等于 ______ .
            • 3.
              已知点\(P\)是\(O\)的一点,过\(P\)作\(O\)的线\(A\),\(PB\)切为\(A\),,过\(P\)作一割线交圆\(O\)于点\(EF\),若\(PA=PF\)取\(PF\)的中点,接\(AD\),并延长交于.
              证:\(PB2AD⋅DH\).
            • 4.
              如图,若\(Ω\)是长方体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)被平面\(EFGH\)截去几何体\(EFGHB_{1}C_{1}\)后得到的几何体,其中\(E\)为线段\(A_{1}B_{1}\)上异于\(B_{1}\)的点,\(F\)为线段\(BB_{1}\)上异于\(B_{1}\)的点,且\(EH/\!/A_{1}D_{1}\),则下列结论中不正确的是\((\)  \()\)
              A.\(EH/\!/FG\)
              B.四边形\(EFGH\)是矩形
              C.\(Ω\)是棱柱
              D.\(Ω\)是棱台
            • 5.
              如图所示,\(\triangle ABC\)内接于圆\(O\),\(D\)是\( \hat BAC\)的中点,\(∠BAC\)的平分线分别交\(BC\)和圆\(O\)于点\(E\),\(F\).
              \((\)Ⅰ\()\)求证:\(BF\)是\(\triangle ABE\)外接圆的切线;
              \((\)Ⅱ\()\)若\(AB=3\),\(AC=2\),求\(DB^{2}-DA^{2}\)的值.
            • 6.
              如图,在直角梯形\(ABCD\)中,\(DC/\!/AB\),\(CB⊥AB\),\(AB=AD=a\),\(CD= \dfrac {a}{2}\),点\(E\),\(F\)分别为线段\(AB\),\(AD\)的中点,则\(EF=\) ______ .
            • 7.
              如图,点\(P\)是▱\(ABCD\)边\(AB\)上的一点,射线\(CP\)交\(DA\)的延长线于点\(E\),若\( \dfrac {AP}{CD}= \dfrac {2}{5}\),则\( \dfrac {S_{\triangle AEP}}{S_{\triangle BCP}}=\) ______ .
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