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Fourth grade math test questions
1.

∠∠DAC =∠∠FBC (the outer angle of the inscribed quadrangle of a circle is equal to the inner diagonal)

EAD=∠BAF=∠BCF

∠DAC=∠EAD

∴∠FBC=∠BCF

∴FB=FC

2.

∵∠ FAC +∠ FBC = 180 (diagonal complementation of inscribed quadrangles of a circle)

∠FCD+∠BCF= 180

FBC=∠BCF

∴∠FAC=∠FCD

And ∵∠AFC is the male angle.

∴△FAC∽△FCD

∴FC/FD=FA/FC

Namely FC? =FD*FA

FC = FB

∴FB? =FD*FA