An isosceles trapezoid circumscribed about a circle with a length of 16 points Find the length of the smaller of the bases

An isosceles trapezoid circumscribed about a circle with a length of 16 points Find the length of the smaller of the bases of the trapezoid if the length of its lateral side is 20.

Given:
ABCD – r / b trapezoid
AB = DC = 20
l = 16п
Find: ВС -?
Decision
1) l = 2пR
l = 16п
16п = 2пR / we reduce /
R = 8.
2) The diameter of the circle is equal to the height drawn from the corner C to the base AD;
triangle СНD – rectangular (СН – height)
CH = circle diameter = 2R = 16
СD = 20 (by condition)
HD = √ (DC ^ 2 – CH ^ 2) = √ (400 – 256) = 12
3) We will draw from the angle B the height of the BM to the AD
since the circle is inscribed in a quadrangle, then the sums of the opposite sides are equal, i.e. AB + CD = BC + AD = 40
BC + AD = BC + AM + MH + HD = 40
AM = HD = 12
MH = BC
2BC + 2AM = 40
AM = 12
2BC = 40 – 24
BC = 8
Answer: BC = 8.