Answer to Question #240279 in Geometry for 0.0

Question

ABCD is a right trapezoid (\angle A = 90°), its diagonals intersect at point G. The circle with diameter AB is tangent to lateral side CD of the trapezoid at point H. Find the length of base BC provided that GH = 5, AD = 7.

Answer 1

Since AD=7 cm

and GH=5cm we can see the semi circle in trapezoid whose radius is 5 cm

AB=10cm ( because its the diameter of circle)

since $\angle A=90\degree$

and AD is parallel to BC

so $\angle B=90\degree$

this show that AD is parallel to BC

AD=7cm so BC=7cm