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.