It is given a rhombus of side length a = 20 cm. Touchpoints of inscribed circle divided his sides into sections a1 = 13 cm and a2 = 7 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.

Correct answer:

r =  9.5 cm
u1 =  32.2 cm
u2 =  23.7 cm

Step-by-step explanation:

a1=13 cm a2=7 cm  a=a1+a2=13+7=20 cm  r2 = a1 a2  r=a1 a2=13 7=91=9.5 cm
(u1/2)2 = r2+a12  u1=2 r2+a12=2 9.53942+132=4 65=32.2 cm
(u2/2)2 = r2+a22  u2=2 r2+a22=2 9.53942+72=4 35=23.7 cm

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