Question

Circle J is inscribed in isosceles trapezoid ABCD as shown. Points E, F, G and H are points of tangency. The length of AB is 10 cm. The length of DC is 20 cm. What is the length, in cm, of BC? (image attached)A. 5B. 10C. 15D. 30thank you ! :)

Answer 1

Since ABCD is an isosceles trapezoid, the points E and G are midpoint of the sides AB and CD, respectively.

That means we have AE = BE = 5 cm and CG = GD = 10 cm.

Since the points E, F, G and H are tangent points, we also have BE = BF and CF = CG.

Therefore the length of BC is:

`\begin{gathered} BC=BF+CF\\ \\ BC=BE+CG\\ \\ BC=5+10\\ \\ BC=15\text{ cm} \end{gathered}`

So the correct option is C.