(1)如图1,△ABC中,P是∠ABC与∠ACB的角平分线的交点,写出∠BPC与∠A的关系;(2)如图2,△ABC中,P是∠ABC的角平分线和△ABC的外角∠ACE的角平分线的交点,写出∠BPC与∠A的关系;(3)如图3,△AB
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![(1)如图1,△ABC中,P是∠ABC与∠ACB的角平分线的交点,写出∠BPC与∠A的关系;(2)如图2,△ABC中,P是∠ABC的角平分线和△ABC的外角∠ACE的角平分线的交点,写出∠BPC与∠A的关系;(3)如图3,△AB](/uploads/image/z/12954312-0-2.jpg?t=%EF%BC%881%EF%BC%89%E5%A6%82%E5%9B%BE1%2C%E2%96%B3ABC%E4%B8%AD%2CP%E6%98%AF%E2%88%A0ABC%E4%B8%8E%E2%88%A0ACB%E7%9A%84%E8%A7%92%E5%B9%B3%E5%88%86%E7%BA%BF%E7%9A%84%E4%BA%A4%E7%82%B9%2C%E5%86%99%E5%87%BA%E2%88%A0BPC%E4%B8%8E%E2%88%A0A%E7%9A%84%E5%85%B3%E7%B3%BB%EF%BC%9B%EF%BC%882%EF%BC%89%E5%A6%82%E5%9B%BE2%2C%E2%96%B3ABC%E4%B8%AD%2CP%E6%98%AF%E2%88%A0ABC%E7%9A%84%E8%A7%92%E5%B9%B3%E5%88%86%E7%BA%BF%E5%92%8C%E2%96%B3ABC%E7%9A%84%E5%A4%96%E8%A7%92%E2%88%A0ACE%E7%9A%84%E8%A7%92%E5%B9%B3%E5%88%86%E7%BA%BF%E7%9A%84%E4%BA%A4%E7%82%B9%2C%E5%86%99%E5%87%BA%E2%88%A0BPC%E4%B8%8E%E2%88%A0A%E7%9A%84%E5%85%B3%E7%B3%BB%EF%BC%9B%EF%BC%883%EF%BC%89%E5%A6%82%E5%9B%BE3%2C%E2%96%B3AB)
(1)如图1,△ABC中,P是∠ABC与∠ACB的角平分线的交点,写出∠BPC与∠A的关系;(2)如图2,△ABC中,P是∠ABC的角平分线和△ABC的外角∠ACE的角平分线的交点,写出∠BPC与∠A的关系;(3)如图3,△AB
(1)如图1,△ABC中,P是∠ABC与∠ACB的角平分线的交点,写出∠BPC与∠A的关系;
(2)如图2,△ABC中,P是∠ABC的角平分线和△ABC的外角∠ACE的角平分线的交点,写出∠BPC与∠A的关系;
(3)如图3,△ABC中,P是外角∠MBC与∠BCN的角平分线,写出∠P与∠A的关系.
(1)如图1,△ABC中,P是∠ABC与∠ACB的角平分线的交点,写出∠BPC与∠A的关系;(2)如图2,△ABC中,P是∠ABC的角平分线和△ABC的外角∠ACE的角平分线的交点,写出∠BPC与∠A的关系;(3)如图3,△AB
(1)∠BPC=∠ABC/2 ,∠PCB=∠ACB/2
∠BPC=180-(∠BPC+∠PCB)=180-(∠ABC/2+∠ACB/2)=180-(180-∠A)/2=90+∠A/2
(2)∠PBC=∠ABC/2 ,∠ACP=∠ACE/2 ,∠ACE=180-∠ACB
∠BPC=180-∠PBC-∠BCP=180-∠ABC/2-(∠ACB+∠ACP)=180-∠ABC/2-[∠ACB+(180-∠ACB)/2]=180-∠ABC/2-(90+∠ACB/2)=90-(∠ABC+∠ACB)/2=90-(180-∠A)/2=∠A/2
(3)∠PBC=∠MBC/2 ,∠MBC=180-∠ABC
∠PCB=∠BCN/2 ,∠BCN=180-∠ACB
∠P=180-(∠PBC+∠PCB)=180-(∠MBC+∠BCN)/2=180-(360-∠ABC-∠ACB)/2=180-360/2+(∠ABC+∠ACB)/2=(180-∠A)/2=90-∠A/2
(1)∠BPC=180-1/2(∠ABC+∠ACB)
∠A=180-(∠ABC+∠ACB)
∠BPC=90+1/2∠A
(2)∠ACE=∠A+∠ABC
∠PCE=∠BPC+∠PBC=1/2∠ACE
∠ABC=2∠PBC
∠BPC=1/2∠A
(3)∠P=180-(∠PBC+∠PCB)
=180-1/2(∠MBC+∠BCN)
=...
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(1)∠BPC=180-1/2(∠ABC+∠ACB)
∠A=180-(∠ABC+∠ACB)
∠BPC=90+1/2∠A
(2)∠ACE=∠A+∠ABC
∠PCE=∠BPC+∠PBC=1/2∠ACE
∠ABC=2∠PBC
∠BPC=1/2∠A
(3)∠P=180-(∠PBC+∠PCB)
=180-1/2(∠MBC+∠BCN)
=180-1/2(180-∠ABC+180-∠ACB)
=180-1/2(360-(∠ABC+∠ACB))
=180-1/2(360-(180-∠A))
=90-1/2∠A
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﹙1﹚,∠p=90°+½∠A
﹙2﹚,∠p=½∠A
﹙3﹚,∠p=90°-½∠A
(1):<BPC=90+<A/2
∵∠A+∠ABC+∠ACB=180
∴∠ABC+∠ACB=180-∠A
∵BP平分∠ABC
∴∠PBC=∠ABC/2
∵CP平分∠ACB
∴∠PCB=∠ACB/2
∵∠BPC+∠PBC+∠PCB=180
∴∠BPC=180-(∠PBC+∠PCB)
=180-(∠ABC/2+∠ACB/2)
=180-(∠ABC+∠AC...
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∵∠A+∠ABC+∠ACB=180
∴∠ABC+∠ACB=180-∠A
∵BP平分∠ABC
∴∠PBC=∠ABC/2
∵CP平分∠ACB
∴∠PCB=∠ACB/2
∵∠BPC+∠PBC+∠PCB=180
∴∠BPC=180-(∠PBC+∠PCB)
=180-(∠ABC/2+∠ACB/2)
=180-(∠ABC+∠ACB)/2
=180-(180-∠A)/2
=90+∠A/2
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1,a=180度-2p 因为180-1/2∠ABC-1/2∠ACB=∠P且180-∠ABC-∠ACB=∠A
2,1/2∠ABC+1/2(180度-(180度-∠A-∠ABC))+∠P=180度->∠ABC+1/2∠A+∠P=180度
3,∠ABC+∠A+∠ACB=180度,1/2(180度-∠ABC)+1/2(180度-∠ACB)+∠P=180度->2∠A+∠P=180度
<p=180-<pac-,pca <p=180-1/2(<b-<c) <a=180-<b-<c <p-<a=180-1/2(<b-<c)&...
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<p=180-<pac-,pca <p=180-1/2(<b-<c) <a=180-<b-<c <p-<a=180-1/2(<b-<c) -180-<b-<c =1/2(<b-<c) 2. <a+1/2<b=<p+1/2<ace <a+1/2<b=<p+1/2(<a+<b) <a=1/2<a+<p 3. <p=180-<pbc-<pcn <p=180-1/2<mbc -1/2<ncb <p=180-1/2(<a+<acb)-1/2(<a+<abc) <p=180-1/2(<a+<acb+<a+<abc) <p=180-1/2(<a+180) <p=180-1/2<a-90 <p=90-1/2<a
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