Quadrilateral 78874

Given is a quadrilateral ABCD inscribed in a circle, with the diagonal AC being the circle's diameter. The distance between point B and the diameter is 15 cm, and between point D and the diameter is 18 cm. Calculate the radius of the circle and the perimeter of the quadrilateral ABCD.

Correct answer:

r =  18 cm
o =  99.7 cm

Step-by-step explanation:

h1=15 cm h2=18 cm  AC=2r  x+y=r z+w=r  h12 = x (y+z+w) h22 = w (x+y+z)  h12 = x (y+r) h22 = w (r+z)  h12 = (ry) (y+r) h22 = (rz) (r+z)  h12 = r2y2 h22 = r2z2  z=0 r=h22+z2=182+02=18=18 cm  w=rz=180=18 cm  h12=r2y2  152=182y2 y299=0 y1,2=±99=±9.949874371 y1=9.949874371 y2=9.949874371  y=y1=9.9499=3 11 cm9.9499 cm x=ry=189.94998.0501 cm

Our quadratic equation calculator calculates it.

a=h12+x2=152+8.0501217.0236 cm b=h12+(r+y)2=152+(18+9.9499)231.7206 cm c=h22+w2=182+182=18 2 cm25.4558 cm d=h22+(r+z)2=182+(18+0)2=18 2 cm25.4558 cm  o=a+b+c+d=17.0236+31.7206+25.4558+25.4558=99.7 cm

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