如图,在△ABC中内角∠ABC的平分线延长后语∠ACB外角平分线交与点F.如图,在△ABC中,∠ABC等于90º,∠BAC=mº,内角∠ABC的平分线延长后语∠ACB外角平分线交与点F,直线AH‖BF且与射线CF交与点H.
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![如图,在△ABC中内角∠ABC的平分线延长后语∠ACB外角平分线交与点F.如图,在△ABC中,∠ABC等于90º,∠BAC=mº,内角∠ABC的平分线延长后语∠ACB外角平分线交与点F,直线AH‖BF且与射线CF交与点H.](/uploads/image/z/5324194-10-4.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%E5%86%85%E8%A7%92%E2%88%A0ABC%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E5%BB%B6%E9%95%BF%E5%90%8E%E8%AF%AD%E2%88%A0ACB%E5%A4%96%E8%A7%92%E5%B9%B3%E5%88%86%E7%BA%BF%E4%BA%A4%E4%B8%8E%E7%82%B9F.%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0ABC%E7%AD%89%E4%BA%8E90%26ordm%3B%2C%E2%88%A0BAC%3Dm%26ordm%3B%2C%E5%86%85%E8%A7%92%E2%88%A0ABC%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E5%BB%B6%E9%95%BF%E5%90%8E%E8%AF%AD%E2%88%A0ACB%E5%A4%96%E8%A7%92%E5%B9%B3%E5%88%86%E7%BA%BF%E4%BA%A4%E4%B8%8E%E7%82%B9F%2C%E7%9B%B4%E7%BA%BFAH%E2%80%96BF%E4%B8%94%E4%B8%8E%E5%B0%84%E7%BA%BFCF%E4%BA%A4%E4%B8%8E%E7%82%B9H.)
如图,在△ABC中内角∠ABC的平分线延长后语∠ACB外角平分线交与点F.如图,在△ABC中,∠ABC等于90º,∠BAC=mº,内角∠ABC的平分线延长后语∠ACB外角平分线交与点F,直线AH‖BF且与射线CF交与点H.
如图,在△ABC中内角∠ABC的平分线延长后语∠ACB外角平分线交与点F.
如图,在△ABC中,∠ABC等于90º,∠BAC=mº,内角∠ABC的平分线延长后语∠ACB外角平分线交与点F,直线AH‖BF且与射线CF交与点H.
(1)求∠ACH(用含mº的式子表示);
(2)点P为射线CF上一点,且∠APC= ½∠ACB ,问:当m分别为何范围的值时,点P在线段CH上?点P在线段CH的延长线上?并说明理由.
如图,在△ABC中内角∠ABC的平分线延长后语∠ACB外角平分线交与点F.如图,在△ABC中,∠ABC等于90º,∠BAC=mº,内角∠ABC的平分线延长后语∠ACB外角平分线交与点F,直线AH‖BF且与射线CF交与点H.
(1)∵在△ABC中,∠ABC = 90º,∠BAC = mº
∴∠ACB外角∠ACG = 90º + mº
∵CH 为 ∠ACG 的角平分线
∴∠ACH = 1/2 ∠ACG = 1/2 (90º + mº) = 45º + 1/2mº
(2)∵∠ABC = 90º,BF 是∠ABC的平分线
∴∠ABF = 45º
∵AC 交 BF 于点E
∴∠BFC + ∠ACH = ∠ABF + ∠BAC
∴∠BFC = 45º + mº - (45º + 1/2mº) = 1/2 mº
∵AH // BF
∴∠AHC = ∠BFC = 1/2 mº
∵在△ABC中,∠ABC = 90º,∠BAC = mº
∴∠ACB = 180º - (90º + mº) = 90º - mº
∴∠APC = 1/2∠ACB = 45º - 1/2mº
∵ 要使Rt△ABC存在,
∴ 0º < mº < 180º - 90º = 90º①
当点P恰与点H重合时
∵∠APC = ∠AHC = 1/2 mº = 45º - 1/2mº
∴ m = 45
当点P在线段CH上时
∵由①可知
∠AHC =1/2 mº < 90º ,
∠ACH = 45º + 1/2mº < 90º ,
∠AHC = 1/2 mº < 45º + 1/2mº = ∠ACH
∴∠AHC < ∠APC < 90º
∴ 0 < m < 45
当点P在线段CH的延长线上时
∵∠APC < ∠AHC,综合①
∴ 45 < m < 90