7 Trapezoid KLMN has sides KL80 units LM 60 units MN22 unit

-7. Trapezoid KLMN has sides KL-80 units, LM = 60 units, MN-22 units, and KN- 65 units, with KL parallel to MN. A semicircle with center A on KL is drawn tangent to both sides KN and ML. What is the length of segment KA?

Solution

Point A is on side KL ....and semicircle drawn with center A on KL is drawn tangent to both sides KN and ML.. this implies that K and L are two opposite point on circle ... So KL is the diameter of circle and A is the mid point of KL... So length of KA = 80/2 = 40 units.