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 1
0 cm. The length of DC is 20 cm. What is the length, in cm, of BC?
1 answer:
Answer:
15cm
Step-by-step explanation:
Theorem: All tangents to a circle from the same point are equal.
Sine E, F, G and H are points of Tangency, by the theorem above:
- EB=BF
- FC=GC
The diameter line EC divides the Isosceles Trapezoid into two equal parts.
Therefore:
- EB=10/2=5cm
- GC=20/2=10cm
We then have by the equality above that:
- BF=5cm
- FC=10cm
BC=BF+FC
=5+10
=15cm
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