Rhombus

It is given a rhombus of side length a = 19 cm. Touch points of inscribed circle divided his sides into sections a1 = 5 cm and a2 = 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.

Correct result:

r =  8.4 cm
u1 =  19.5 cm
u2 =  32.6 cm

Solution:

a1=5 cm a2=14 cm  a=a1+a2=5+14=19 cm  r2=a1 a2  r=a1 a2=5 14=70=8.4 cm
(u1/2)2=r2+a12  u1=2 r2+a12=2 8.36662+52=2 95=19.5 cm
(u2/2)2=r2+a22  u2=2 r2+a22=2 8.36662+142=2 266=32.6 cm



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