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?

Answer 1

15cm

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