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Nankai high school middle school mathematics
1, connecting BD and AC to O, and vertically dividing BD and AC. According to trigonometric function, AO=2√5, BO=√5, sinCAB=√5/5? The distance from C to AB is AC*sinCAB=4√5*√5/5=4.

2. Similarly, if the speed in the AC direction is √5, the speed in the horizontal direction is 2 and the speed in the vertical direction is 1. (physical decomposition direction), obviously the maximum t is 4√5/√5=4, that is, t is 0,4, FG//AC (tangents are all equal to 1/2).

0< when t "1",it is easy to get the PHF area of the triangle =0.8( 1-t)2, the overlapping area S= 1-0.8( 1-t)2 (in the following cases), when t=0. T is at 3 o'clock, S= 1.

3<t<4, GH=t-3, the PHF area of the easily obtained triangle =(t-3)2, and the overlapping area S= 1-(t-3)2. When t=4, S=0.

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