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…

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asked Sep 16, 2023 235k views

1 Answer

Raelynn · Answer 1 · 2023-09-20T07:19:28+0000

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.