Question #88ad2

1 Answer
CW
Jan 13, 2018

see explanation.

Explanation:

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Recall that the tangents to a circle from an external point are equal in length,
#=> AM=AN, BM=BP, CN=CP#
#AM=AB+BM#,
#AN=AC+CN#,
#BC=BP+CP=BM+CN#
let #p# be the perimeter of #DeltaABC#,
#=> p=AB+BC+CA#,
#=> p=AB+(BM+CN)+CA#
#=> p=(AB+BM)+(CN+CA)#
#=> p=AM+AN#
#=> p=2AM#
#=> AM=1/2p# (proved)

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