解：如图3，

∵ $∠ A G D = ∠ F ， ∠ A G D + ∠ D G E = 180 °$ ，

$∴ ∠ D G E + ∠ F = 180 ° ，$

∴点D、G、E、F共圆，

$∵ ∠ E C F + ∠ D C E = 180 ° ，$ $∠ F = ∠ E C F ，$

$∴ ∠ D G E = ∠ D C E ，$

$∴ △ G D E ∽ △ C D E$ 或 $△ G D E ∽ △ C E D ，$

当 $∴ △ G D E ∽ △ C D E$ 时， $∠ G D E = ∠ C D E ，$

$\begin{array}{l} ∵ D E = D E ， \\ ∴ △ C D E ≌ △ G D E （ A A S ）， \\ ∴ D G = D C ， \\ ∵ ∠ A D E = 90 ° ， \\ ∴ ∠ A D B + ∠ E D C = ∠ A D G + ∠ G D E = 90 ° ， \\ ∴ ∠ A D B = ∠ A D G ， \\ ∵ ∠ A B D = ∠ E C F = ∠ F ， \\ ∴ ∠ A B D = ∠ A G D ， \\ ∵ A D ＝ A D ， \\ ∴ △ A B D ≌ △ A G D （ A A S ）， \\ ∴ D B = D G ， \\ ∴ B D = C D = \frac{1}{2} B C = 17 ， \end{array}$

当 $△ G D E ∽ △ C E D$ 时，如图4，

$\begin{array}{l} ∴ ∠ G D E = ∠ D E C ， ∠ G E D = ∠ C D E ， \\ ∴ D G ∥ C E ， C D ∥ G E ， \end{array}$

∴四边形 $C D G E$ 是平行四边形，

由（1）（2）知，

\begin{array}{l} \begin{array}{l} A K = 8 ， D K = x - 6 ， C D = 34 - x ， △ A K D ∽ △ D T E ， \\ ∵ A B ∥ C E ， A E ∥ B C ， A K ⊥ B F ， E T ⊥ B F \end{array} \\ ∴ E T = A K = 8 ， C T = B K = 6 ， D T = 34 - x + 6 = 40 - x ， \\ ∴ \frac{A K}{D K} = \frac{D T}{E T} ， \\ ∴ \frac{8}{x - 6} = \frac{40 - x}{8} \\ ∴ x = 8 ， \end{array} MathType@MTEF@5@5@+=   feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn   hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDhatCvAUfeB   Sn0BKvguHDwzZbqegCRWl7marqqtubsr4rNCHbqegSSZmxoasaacH8   srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea   0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaaba   qaciGacaGaaeqabaWaaqaafaGbaOqaauaabaqafeaaaaabaeqabaae   aaaaaaaaa8qacaWGbbGaam4saiaak2dacaaI4aGaaOid=laadseaca   WGlbGaaOypaiaadIhacqGHsislcaaI2aGaaOid=laadoeacaWGebGa   eyypa0JaaG4maiaaisdacqGHsislcaWG4bGaaiilaiabloBjwjaadg   eacaWGlbGaamiraiaak2JicqWIZwIvcaWGebGaamivaiaadweacaGI   m8pabaGaaWynIiaadgeacaWGcbGaaOyjIiaadoeacaWGfbGaaWid=l   aadgeacaWGfbGaaOyjIiaadkeacaWGdbGaaWid=laadgeacaWGlbGa   eyyPI4LaamOqaiaadAeacaGGSaGaamyraiaadsfacqGHLkIxcaWGcb   GaamOraaaapaqaa8qacqGH0icxcaWGfbGaamivaiaak2dacaWGbbGa   am4saiaak2dacaaI4aGaaOid=laadoeacaWGubGaaOypaiaadkeaca   WGlbGaaOypaiaaiAdacaGIm8VaamiraiaadsfacaGI9aGaaG4maiaa   isdacqGHsislcaWG4bGaey4kaSIaaGOnaiabg2da9iaaisdacaaIWa   GaeyOeI0IaamiEaiaacYcaa8aabaWdbiabgsJiCnaalaaabaGaamyq   aiaadUeaaeaacaWGebGaam4saaaacaGI9aWaaSaaaeaacaWGebGaam   ivaaqaaiaadweacaWGubaaaiaakYW=a8aabaWdbiabgsJiCnaalaaa   baGaaGioaaqaaiaadIhacqGHsislcaaI2aaaaiaak2dadaWcaaqaai   aaisdacaaIWaGaeyOeI0IaamiEaaqaaiaaiIdaaaaapaqaa8qacqGH   0icxcaWG4bGaaOypaiaaiIdacaGIm8paaaaa@AB92@

综上所述：BD＝17或8．

28.2 解直角三角形及其应用 人教版九年级下册同步练习

28.2 解直角三角形及其应用人教版九年级下册同步练习