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...Geometry problems solutions alvin zou april th let r be the radii of circles centered at a b c respectively we then have following system equations bc ax ay ra rc solving yields and denote bac bad is our unknown by ac ad get dac cad thus acd that can now abc using condition cab draw perpendicular from center semicircle to ce call this point x notice radius since abcd square ea are tangents as well cx andex wecanpythagoreantheoremedc withlegs de eaanddc with hypotenuse diagram m d it given amd cmd cdm alternate interior angles ab k dc usethebaseangletheoremtoshowdc mc weknowthat abcdisarectangle so follows bmc triangle if measure f foot g quickly triangles abe efg gfd congruent because equal sides right angle ssa side length pythagorean theorem first e dec dbc quadrilateral debc cyclic which result due same inscribed arcs q an equilateral on line such cd andpointaanddaredistinct bcd isosceles also cbd abd abdisa drawing l n ablm mlb mlc cml anm alcn man amn vertical collinear i y feet a...