maths (circle)

2008-03-09 11:14 pm

http://xs.to/xs.php?h=xs125&d=08100&f=maths167.png

In the picture, a circle is inscribed in triangle ABC. The circle touches AB, BC and CA at P, A and R respectively. If angle BOC = 115 , find

a)angle BAC

b)angle PQR

can anyone help me??

回答 (1)

用戶4820

2008-03-10 12:08 am

✔ 最佳答案

以下題解不保證是最快且最方便的方法，只作參考。
a)Join OQ ,OP, OR, OA,
∠QOC = ∠ROC(tan. from ext. pt.)
∠QOB = ∠POB(tan. from ext. pt.)
∴∠QOC + ∠QOB + ∠ROC + ∠POB = 115∘ *2 = 230∘
∴∠POR = 360∘ - 230∘ = 130∘(∠s at a pt.)
∠POA = ∠ROA = 130∘/2 = 65∘ (tan. from ext. pt.)
∠APO = 90∘(tangent⊥ radius)
∠PAO = 180∘-90∘-65∘ = 25∘(∠sum of △)
∠PAO = ∠RAO (tan. from ext. pt.)
∴∠BAC = 50∘

b)∵∠POR = 130∘
∴∠PQR = 65∘ (∠ at centre = 2 ∠at ◎CE)

2008-03-09 16:09:34 補充：
&compfn; 為度數的符號，不知什麼原因顯示不到，你無視它們吧

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