How to Find the Tangent of Angle Alpha in the Semicircle | Geometry | Math

[@soli9mana-soli4953]

setting 6 the diameter of the semicircle, the radius R of the small circle can be find with (3-R)² = R² + 1² R = 4/3 tan α/2 = 1/3 tan 2*(α/2) = tan α = (2*1/3)/1-(1/3)² = 3/4

[@じーちゃんねる-v4n]

A(0,0) B(3,0) (3/2-r)^2=1/4+r^2 r=2/3 distance AC:y=mx and (2,2/3) is 2/3 (2/3-2m)/√(1+m^2)=2/3 tanα=m=3/4

[@じーちゃんねる-v4n]

A(0) B(3) (3/2-r)^2=1/4+r^2 r=2/3 M(2+(2/3)i=(2/3)(3+i)) (3+i)^2=8+6i tanα=6/8=3/4