In the isosceles trapezoid ABCD, the angle B is 60 degrees, ad is parallel to BC, and the angle BAC is equal to 90 degrees. The median line length of the isosceles trapezoid is 12cm. Find the circumference of the isosceles trapezoid

In the isosceles trapezoid ABCD, the angle B is 60 degrees, ad is parallel to BC, and the angle BAC is equal to 90 degrees. The median line length of the isosceles trapezoid is 12cm. Find the circumference of the isosceles trapezoid

Because the angle BAC is equal to 90 degrees, so the angle B is the bottom angle, so the angle bad = angle d = 120 degrees, so the angle DAC = angle DCA = 30 degrees, so Da = DC = AB, because the angle DCB = 60 degrees, so the angle ACB = 30 degrees, so BC = 2Ab, that is BC = 2da

The median line of circle circumscribed isosceles triangle trapezoid ABCD is Mn = 20cm, and the perimeter of this isosceles triangle is calculated

According to the fact that the median line of the trapezoid is equal to half of the sum of the two bottoms, the sum of the two bottoms of the trapezoid is equal to twice of the median line of the trapezoid, that is 40cm;
According to the fact that the sum of the two opposite sides of the circumscribed quadrilateral is equal, the sum of the two waists of the trapezoid is equal to the sum of the two bottoms, that is 40cm
Then the circumference of trapezoid is equal to 40 + 40 = 80 (CM)

Circle O is inscribed on isosceles trapezoid ABCD. If the median line of trapezoid is 12cm, what is the circumference of trapezoid? (no figure,

First, AB + CD = 2 * median = 24
Find the second waist AD / BC
A vertical line passing through the center of a circle and making a tangent point (E on CD, f on BC, G on AB, h on AD)
It is proved that OEC and OFC are congruent and CF = CE is obtained
Similarly, it is proved that BF = BG, Ag = ah, DH = De
AD+BC=AH+DH+BF+CF=AG+DE+BG+CE=(AG+BG)+(DE+CE)=AB+CD=24
Trapezoid perimeter = 24 + 24 = 48CM

The circumference of the circle circumscribed isosceles trapezoid ABCD is 40 cm, and the median line length of this trapezoid is calculated

To give a circle is usually to lead the radius from the center of the circle. This problem is to make a vertical radius from the center of the circle to the four sides of the T-shape [the picture can't be published]. After that, you can get the upper bottom + lower bottom = 2 * waist, so the upper bottom + lower bottom = perimeter / 2 = 20, and the median line = (upper bottom + lower bottom) / 2 = 10cm