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Solution: estABlish a rectangular coordinate system with the center o of the semicircle as the coordinate origin and the straight line ab as the x axis, a

Math problems in the third grade circle

Solution: estABlish a rectangular coordinate system with the center o of the semicircle as the coordinate origin and the straight line ab as the x axis, a

Math problems in the third grade circle

Solution: estABlish a rectangular coordinate system with the center o of the semicircle as the coordinate origin and the straight line ab as the x axis, as shown in the above figure.

then what The equation of semicircle o is: x? +y? = 1? ( 1≥y≥0)

Let the coordinates of point C be (a, b), then D(-a, b)? ,CD=2a? Among them? (0≤a≤ 1,0≤a≤ 1)

Substitute D(-a, b) into the semicircle O equation to get a? +b? = 1,b? = 1-a?

∵AD=BC=x? (x≥0)

∴x? =b? X for +( 1-a)? = 1-a? +( 1-a)? =2-2a,? 2a=2-x?

And AB=2.

∴y=2+2x+2-x? =? -? x? +2x+4

∫0≤a≤ 1,x=√(2-2a)

∴0≤x≤√2

∴y=-? x? +2x+4 (0≤x≤√2)