Question

(17 points) Determine if line AB is tangent to the circle

Answer 1

1. If AB is tangent to the circle, then

$18^2=(2\cdot7.2)^2+10.8^2$

We have

$18^2=324$

$(2\cdot7.2)^2+10.8^2=324$

so AB is indeed tangent to the circle.

2. The unlabeled leg is another radius of the circle so it has length 8. Then if AB is tangent to the circle,

$(10+8)^2=8^2+15^2$

but we have

$(10+8)^2=324$

$8^2+15^2=289$

so that cannot be a right triangle and AB is not tangent to the circle.