About circles 1

2010-07-27 6:18 pm
5 marks. please show steps. please answer. thank you.
link: http://www.sendspace.com/file/052s6x

回答 (1)

2010-07-27 6:43 pm
✔ 最佳答案
Join OC, then OC is perp. to PQ since radius is perp. to radius at the point of touching.

Thus:

∠OCP = ∠QOP = 90

∠CPO = ∠OPQ (Common ∠s)

Hence △OCP ~ △QOP (AAA)

Also

∠OCQ = ∠QOP = 90

∠CQO = ∠OQP (Common ∠s)

Hence △OCQ ~ △QOP (AAA)

So we have △OCP ~ △QCO

Conclusion: ∠OPC = ∠QOC = ∠COB
參考: Myself


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