MR-529 / 14. problem

Length of the sides of cyclic trapezoid are: AB = 5 cm, BC = 2,5 cm, CD = 2 cm and DA = 2,5 cm.

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a) Calculate the angles of the trapezoid!
b) Determine the ratio of ABC and ACD triangles!
c) The inner angles of the trapezoid are marked with an arc of 5 mm radius. Calculate the sum of the four arc lengths!

a) BT=5-22=1,5
BCTcosβ=BTBC=1,52,5=0,6
β=arccos0,6
β=53,13°
α=β=53,13°
α+γ=180°
γ=180°-α=180°-53,13°
γ=126,87°
δ=γ=126,87°
b) BCT2,52=m2+1,52
m2=2,52-1,52
m2=522-322=254-94=164=4
m=2
TABC=AB·m2=5·22=5cm2
TACD=CD·m2=2·22=2cm2
TABCTACD=52
c) α+β+γ+δ=360°
l=2rπ=2·0,5·π
l=π cm

Ez tudnod kell igen

a) α=β=53,13°, δ=γ=126,87°b) TABCTACD=52c) l=π cm