A circle is inscribed in an isosceles trapezoid. It is known that the difference between the bases of the trapezoid

A circle is inscribed in an isosceles trapezoid. It is known that the difference between the bases of the trapezoid is 12 cm, and the side side is 24 cm. Find the smaller base.

GIVEN:
trapezium AВСD
AB = СD = 24
AD-ВС = 12
BC =?
DECISION
a circle can be inscribed in any four gon if the sums of the opposite sides are equal. i.e
BP + BC = AB + СD
AB + СD = 24 + 24 = 48 (according to conv)
we express AD:
AD-ВС = 12
AD = 12 + BC
let’s make the equation:
12 + BC + BC = 48
2BC = 36
BC = 18 cm
answer: 18 cm