Tangent length theorem 1. In the trapezoid ABCD, ad ‖ BC, ∠ ABC = 90 ° the semicircle o with ab as diameter cuts CD at point M. if the trapezoid has an area of 10 square centimeters and a perimeter of 14cm, what is the radius of semicircle o? 2. The side length of square ABCD is a, AE cuts the semicircle with diameter BC to e, intersects DC to F, and finds CF: FD

Tangent length theorem 1. In the trapezoid ABCD, ad ‖ BC, ∠ ABC = 90 ° the semicircle o with ab as diameter cuts CD at point M. if the trapezoid has an area of 10 square centimeters and a perimeter of 14cm, what is the radius of semicircle o? 2. The side length of square ABCD is a, AE cuts the semicircle with diameter BC to e, intersects DC to F, and finds CF: FD

(1)AD=DM,BC=CM
Let AD + BC = DM + MC = DC = x, radius r of semicircle o,
Then: ab = 2R
Then: perimeter = 2R + 2x = 14
Area = x * (2R) / 2 = RX = 10
The solution is r = 2 or r = 5
When r = 5, x = 2