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

Given:

ABCD is a right trapezoid (angle A = 90°)

GH = 5

AD = 7

the semi circle in trapezoid whose radius is 5 cm

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

so ∠A = 90°

and AD is parallel to BC

∠B = 90°

So its show that AD is parallel to BC

AD=7cm so BC=7cm

Hence the length of BC is 7cm