HKMO 05-06 (10)

2009-05-01 1:44 am

回答 (1)

2009-05-01 1:59 am
✔ 最佳答案
Triangle PAM congruent triangle QMB (SAS).
So PM = MQ = sqrt ( 1^2 + 3^2) = sqrt 10.
Angle AMP + angle PMQ + angle QMB = 180 degree (angles on a st. line)
but angle AMP + angle QMB = 90 degree, therefore angle PMQ is a rt. angle.
therefore PM^2 + MQ^2 = (2x)^2
10 + 10 = 4x^2
x = sqrt 5.



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