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?

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:

The diameter line EC divides the Isosceles Trapezoid into two equal parts.

Therefore:

We then have by the equality above that:

BC=BF+FC

=5+10

=15cm

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!