Harvey Littleman

From Gogeometry Using Additional points Pythagoras congruent triangles Similar triangles Equilateral triangle Let b=AD=DC and d=BCΔACB and ΔBCD are similar since ∠BAC=∠DBC=x and ∠BCD=∠BCAThen AC/BC=CB/CD=AB/BD => 2b/d=d/b => d=b√2 Define C’ such as DC’ ⊥ AC and DC’=b∠BDC=∠ADC – π/4= π – π/4 = 3 π/4∠BDC’=∠BDA + ∠ADC’ = π/4 […]

Gogeometry Problem 001

From Gogeometry Using : Additional points Similar triangles •ΔABC is isosceles and right in B => BA=BC and ∠BAC=∠BCA=Π/4 • Define G in AC such as AB=AG => ΔBAG is isosceles in A •Define H intersection of AD and BG •∠BAH=∠GAH=Π/4/2=Π/8  and HB=HG and ∠AHB=∠AHG=Π/2 •and ∠ABH=∠AGH and ∠ABH+ ∠BAH […]

Gogeometry Problem 975

ΔABC right triangle in C Define r its inradius, a=BC,b=AC and c=A PCRO is square => PC=CR=r AC et AB tangents to the circle=>AP=AQ, BQ=BR and CP=CR b=AC=AP+PC, a=BC=BR+RC AC+BC=b+a=AP+r+BR+r=2r+AP+BR AP=AQ, BR=BQ => AC+BC=b+a=2r+AQ+BQ=2r+AB=2r+c a+b=2r+c Therefore r=(a+b-c)/2 Define p as the semi-perimeter of the triangle, p=(a+b+c)/2 Therefore r =p-c

Inradius in right triangle