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

Question

asked Sep 25, 2020 200k views

1 Answer

Le Ding · Answer 1 · 2020-09-29T03:26:21+0000

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.